Answers
Answer:
4 m/s
Explanation:
To find the velocity at t = 8 seconds, we will use the following equation:
\(v_f=v_i+at\)Where vf is the final velocity, vi is the initial velocity, a is the acceleration and t is the time.
From t = 0 seconds to t = 3 seconds, we have an acceleration of 6 m/s², so we can calculate the velocity at t = 3 seconds as:
\(\begin{gathered} v_f=-4m/s+6m/s^2(3\text{ s)} \\ v_f=-4\text{ m/s + 18 m/s} \\ v_f=14\text{ m/s} \end{gathered}\)Now, from t = 3 seconds to t = 8 seconds, the acceleration is equal to -2 m/s². So we need to use the same equation but this time, the initial velocity will be 14 m/s and the time will be 5 seconds because t = 8 s - 3 s = 5s. Then, we get:
\(\begin{gathered} v_f=14m/s-2m/s^2(5s) \\ v_f=14\text{ m/s - 10 m/s} \\ v_f=4\text{ m/s} \end{gathered}\)Therefore, the velocity at t = 8 seconds is 4 m/s
Related Questions
hello I need help with this question it does not make sense and has very limited information.
Answers
First, use Newton's Second Law on each mass.
Mass 1.\(T-W_1=m_1a\)Mass 2.\(\Sigma F_y=m_2a\to W_2-T=m_2a_{}\)Solve the second equation for T.
\(T=W_2-m_2a\)Combine the equations.
\(W_2-m_2a-W_1=m_1a_{}\)But the weight force is mg.
\(m_2g-m_2a-m_1g=m_1a\)Solve for a.
\(\begin{gathered} m_2g-m_1g=m_1a+m_2a \\ a(m_1+m_2)=m_2g-m_1g \\ a=\frac{m_2g-m_1g}{m_1+m_2} \end{gathered}\)Let's say the masses are m_1 = 2 kg and m_2 = 5 kg.
\(\begin{gathered} a=\frac{5\cdot9.8-2\cdot9.8}{2+5} \\ a=\frac{49-19.6}{7} \\ a=\frac{29.4}{7} \\ a=4.2\cdot\frac{m}{s^2} \end{gathered}\)Therefore, the acceleration of the system is 4.2 m/s^2.
The drawing shows three identical springs hanging from the ceiling. Nothing is attached to the first spring, whereas a 4.50-N block hangs from the second spring. A block of unknown weight hangs from the third spring. From the drawing, determine (a) the spring constant (in N/m) and (b) the weight of the block hanging from the third spring
Answers
Answer:
a. 30 N / m
b. 9.0 N
Explanation:
Given that
Unstretched length of the spring, \(L_o\) = 20.0cm = 0.2m
a) When the mass of 4.5N is hanging from the second spring, then extended length Is
\(L_1\) = 35.0cm = 0.35m
So, the change in spring length when mass hangs is
\(x = L_1 - L_o\)
= (0.35 - 0.20) m
= 0.15m
As spring are identical
Let us assume that the spring constant be "k", so at equilibrium
Restoring Force on spring = Block weightage
kx = W = 4.50
\(k= \frac{4.50}{x} = \frac{4.50}{0.15}\)
= 30 N / m
b) Now for the third spring, stretched the length of spring is
\(L_2\) = 50cm = 0.5m
So, the change in spring length is
\(x'= L_2 - L_o\)
= (0.5-0.20)m
= 0.30m
At equilibrium,
Restoring Force on spring = Block weightage
Now using all mentioned and computed values in above,
\(W'= kx'\)
= 30(0.3)
= 9.0 N
which can occur in a physical change
Answers
Answer:
A physical change involves a change in physical properties. Examples of physical properties include melting, transition to a gas, change of strength, change of durability, changes to crystal form, textural change, shape, size, color, volume and density.
Explanation:
In 1.0 second, a battery charger moves 0.50 C of charge from the negative terminal to the positive terminal of a 1.5 V AA battery.
Part A:
How much work does the charger do? Answer is 0.75 J
Part B:
What is the power output of the charger in watts?
Answers
Answer:
W = Q * V work done on charge Q
A. W = .5 C * 1.5 V = .75 Joules
B. P = W / t = .75 J / 1 sec = .75 Watts
Activity 1: UNITS OF MEASUREMENT
I. Identify the quantity described by the following units of measurement. Copy and write your answer on one whole sheet of paper.
1. meter per second = _________ 11. joule = ____________
2. meter = _________ 12. Kilogram = ____________
3. second = _________ 13. Cubic meter = _________
4. meter per second squared = ____ 14. Mole = ____________
5. square meter = _________ 15. Kilogram per cubic meter=
6. mass = _________ 16. Watt = ____________
7. newton = _________ 17. Ampere = ____________
8. kelvin = _________ 18. Hertz = ____________
9. volt = _________ 19. Coulomb = ____________
10. candela = __________ 20. Pascal = ____________
Answers
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Relative density
What is relative density ind question due
9/16/21
Answers
Answer:
9
Explanation:
i guess so
can you put a brainliest in me
Answer:
hope this helps
Explanation:
Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest; for gases, the reference is air at room temperature.
A bicycle slows down uniformly from vi=8.40 [m/s] to rest over a distance of 115 [m]. Each wheel and tire has an overall diameter of 0.68 [m]. Determine the magnitude of the angular acceleration of the wheel. Give your answer in units of radians per second squared.
Answers
A bicycle slows down uniformly from vi=8.40 [m/s] to rest over a distance of 115 [m]. Each wheel and tire has an overall diameter of 0.68 [m]. The magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².
To determine the magnitude of the angular acceleration of the wheel, we need to first calculate the change in angular velocity and the time taken to come to rest. Then we can use these values to find the angular acceleration.
Calculate the initial angular velocity:
The initial linear velocity of the bicycle wheel is given by the formula v = ω * r, where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
The radius of the wheel is half the diameter, so r = 0.68 m / 2 = 0.34 m.
Given the initial linear velocity vi = 8.40 m/s, we can calculate the initial angular velocity ωi:
vi = ωi * r
ωi = vi / r
Calculate the final angular velocity:
The final angular velocity of the wheel is 0 rad/s since it comes to rest.
ωf = 0 rad/s
Calculate the change in angular velocity:
The change in angular velocity (Δω) is given by the formula Δω = ωf - ωi.
Δω = 0 - ωi
Calculate the time taken to come to rest:
To calculate the time taken to come to rest, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Given the initial velocity vi = 8.40 m/s, final velocity vf = 0 m/s, and distance d = 115 m, we can calculate the acceleration a:
vf = vi + at
0 = 8.40 + a * t
We also know that the distance traveled d is related to the initial and final velocities and the time by the formula d = (vi + vf) / 2 * t:
d = (vi + vf) / 2 * t
115 = (8.40 + 0) / 2 * t
From the two equations above, we can solve for the acceleration a and the time t.
Calculate the angular acceleration:
The angular acceleration (α) is given by the formula α = Δω / t.
α = Δω / t
Substitute the values for Δω and t and calculate the angular acceleration.
Therefore, the magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².
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12.
A hiker walks for 5km on a bearing of 053" true (North 53° East). She then turns and
walks for another 3km on a bearing of 107° true (East 17° South).
(a)
Find the distance that the hiker travels North/South and the distance that she travels
East/West on the first part of her hike.
Answers
The hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.
This question involves vector addition, the resolution of vectors, the use of bearings, and trigonometry in the calculation of the hiker's movement.
This may appear to be a difficult problem, but with some visual aid and the proper use of mathematical formulas, the issue can be addressed correctly.
Resolution of VectorThe resolution of a vector is the process of dividing it into two or more components.
The angle between the resultant and the given vector is equal to the inverse tangent of the two rectangular components.
Angles will always be expressed in degrees in the solution.
The sine, cosine, and tangent functions in trigonometry are denoted by sin, cos, and tan.
The tangent function can be calculated using the sine and cosine functions as tan x = sin x/cos x. Also, in right-angled triangles, Pythagoras’ theorem is used to find the hypotenuse or one of the legs.
Distance Travelled North/SouthThe hiker traveled North for the first part of the hike and South for the second.
The angles that the hiker traveled in the first part and second parts are 53 degrees and 17 degrees, respectively.
The angle between the two is (180 - 53 - 17) = 110 degrees.
The angle between the resultant and the Northern direction is 110 - 53 = 57 degrees.
Using sine and cosine, we can calculate the north/south distance traveled to be 5 sin 57 = 4.02 km, and the east/west distance to be 5 cos 57 = 2.93 km.
Distance Travelled East/WestThe hiker walked East for the second part of the hike.
To calculate the distance travelled East/West, we must first calculate the component of the first part that was East/West.
The angle between the vector and the Eastern direction is 90 - 53 = 37 degrees.
Using sine and cosine, we can calculate that the distance travelled East/West for the first part of the hike is 5 cos 37 = 3.88 km.
To determine the net distance travelled East/West, we must combine this component with the distance travelled East/West in the second part of the hike.
The angle between the second vector and the Eastern direction is 17 degrees.
Using sine and cosine, we can calculate the distance traveled East/West to be 3 sin 17 = 0.86 km.
The net distance traveled East/West is 3.88 + 0.86 = 4.74 km.
Therefore, the hiker travelled 4.02 km North/South and 4.74 km East/West during her hike.
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A8 kg ball is held at postam A before being rolled down the ramp below. Asume no energy is lost due to
Position
A
A-5m)
Position
B
(x-2m)
Position
C
As
h-5m
Kinetic Energy
B
h-2.5 m
Gravitational Potential Energy
C
h-0m
Total Energy
Answers
The potential energy of the ball at position A is:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above the ground.
PE(A) = 8 kg * 9.8 m/s^2 * 5 m
PE(A) = 392 J
At position B, the ball has both kinetic and potential energy.
The potential energy of the ball at position B is:
PE = mgh
where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above the ground.
PE(B) = 8 kg * 9.8 m/s^2 * 2.5 m
PE(B) = 196 J
The kinetic energy of the ball at position B is:
KE = (1/2)mv^2
where m is the mass of the ball and v is the velocity of the ball.
Since the ball is rolling down the ramp, we can use the conservation of energy principle to find the velocity of the ball at position B.
The total energy of the ball at position A is:
E(A) = PE(A)
E(A) = 392 J
The total energy of the ball at position B is:
E(B) = PE(B) + KE(B)
E(B) = 196 J + (1/2)(8 kg)v^2
E(B) = 196 J + 4v^2
Since energy is conserved, we have:
E(A) = E(B)
392 J = 196 J + 4v^2
196 J = 4v^2
v^2 = 49 m^2/s^2
v = 7 m/s
The kinetic energy of the ball at position B is:
KE(B) = (1/2)mv^2
KE(B) = (1/2)(8 kg)(7 m/s)^2
KE(B) = 196 J
At position C, the ball has only kinetic energy.
The potential energy of the ball at position C is zero since the ball is at ground level.
The kinetic energy of the ball at position C is:
KE(C) = (1/2)mv^2
KE(C
You walk to the corner store at 2 m/s for a total time of 76 seconds. What is the distance to the store?
Answers
Answer:
152.
Explanation:
2 x 76 = 152
bruh its not that hard
Answer:
152 m
Explanation:
Distance = Speed x Time
\(2 \times 76 \\ 152\)
Thus the distance is equal to 152 m.
Bone has a Young's modulus of about1.8 x 10^10 Pa. Under compression, it canwithstand a stress of about 1.69 x 10^8 Pa be-fore breakingAssume that a femur (thigh bone) is 0.49 mlong, and calculate the amount of compressionthis bone can withstand before breaking.Answer in units of mm.
Answers
Answer:
4.6 mm
Explanation:
The Young's Modulus is defined as
\(Y=P\frac{L_0}{\Delta L}\)Where
Y = Young's Modulus
P = pressure (stress) applied
L0 = inital length
ΔL = change in length
Now in our case, we know that the femur is 0.49 m long (L0 = 0.49) and it can withstand max stress of 1.69 x 10^8 Pa ( P = 1.69 x 10^8 Pa), and Young's Modulus for the bone is 1.8 x 10^10 Pa ( Y = 1.8 x 10^10 Pa ); therefore, the above formula gives
\(1.8\times10^{10}=1.69\times10^8\times\frac{0.49}{\Delta L}\)We have to solve the above equation for ΔL, the amount of compression.
Multiplying both sides by ΔL gives
\(\Delta L\times1.8\times10^{10}=1.69\times10^8\times0.49\)dividing both sides by 1.8 x 10^10 gives
\(\Delta L=\frac{1.69\times10^8\times0.49}{1.8\times10^{10}}\)which we evaluate to get
\(\Delta L=\frac{1.69\times0.49}{1.8}\times\frac{10^8}{10^{10}}\)\(\begin{gathered} \Delta L=4.6\times10^{-3}m \\ \boxed{\Delta L=4.6\; mm\text{.}} \end{gathered}\)Hence, the amount of compression a femur can withstand is 4.6 x 10^-3 m or 4.6 mm.
2 similarities between potential energy and kinetic energy
Answers
Convert into each other and both are energy are 2 similarities between potential energy and kinetic energy .
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is squeezed or extended, its potential energy increases. If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy. It is capable of performing more work when raised. Potential energy is a characteristic of systems rather than of particular bodies or particles; for instance, the system made up of Earth and the elevated ball has greater potential energy as they get further apart.
Potential energy develops in systems having components whose configurations, or relative positions, determine the amount of the forces they apply to one another.
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Three masses hang about a meter stick whose fulcrum is at 20cm. A mass of m1=40.0 kg hangs at the 70.0 cm mark, m2= 30.0 kg hangs at the 30.0 cm mark and mass m3 = 20kg is located at the 50 cm mark. The mass of a metal washer, mw is hanging from the 15cm mark.
a) Find the mass of the metal washer, mw needed to obtain static equilibrium.
b) If the mass in part A is not realistic, then draw a diagram that will render a reasonable value.
c) Complete the problem again when the fulcrum is located at the 50 cm mark.
d) Repeat the problem above when the pivot point(axis of rotation) is located at the 60 cm mark of the meter stick.
Answers
A) Find the mass of the metal washer, mw needed to obtain static equilibrium.
To obtain static equilibrium, the sum of the torques on the meter stick must be zero. This can be expressed mathematically as:
Στ = 0
Where Στ is the sum of the torques and is calculated by:
Στ = r1F1 + r2F2 + r3F3 + rwmw
Where r is the distance of the mass from the fulcrum and F is the force due to gravity acting.
A boat on a river is moving with a steady speed. The engine is running.
What would happen if the engine was turned off?
Answers
If the engine of a boat on a river is turned off while the boat is moving with a steady speed, several things would happen Loss of propulsion,Drifting,Loss of steering control and Potential hazards.
Loss of propulsion: Without the engine running, the boat would lose its power source for propulsion. The boat would gradually slow down and eventually come to a stop unless other external forces, such as currents or wind, continue to move it.
Drifting: Once the boat comes to a stop, it would start to drift with the current of the river or be affected by wind forces. The direction and speed of the drift would depend on the strength and direction of the current or wind.
Loss of steering control: When the engine is turned off, the boat's steering mechanism, such as a rudder, would also lose power. Without the ability to steer, the boat would follow the course determined by the river's current or the wind direction.
Potential hazards: Depending on the surroundings and the current conditions, there could be potential hazards for a boat that is no longer under power. These hazards might include other vessels, obstacles, shallow areas, or strong currents. The boat's crew would need to take appropriate actions to ensure the safety of the boat and its occupants.
It's important to note that the specific behavior of the boat after the engine is turned off can vary depending on factors such as the size and design of the boat, the strength and direction of the current, and the presence of wind or other external forces.
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What is the chemical formula for the iconic compound aluminum oxide (a bond between aluminum and oxygen)
Answers
Answer:
C
Explanation:
just try hahahahahhaah
If 0.5 C charge passes through a wire in 10 seconds, what will be the value of the current flowing through the wire? *
20 mA
30 mA
50 mA
60 mA
Answers
Answer:
electric current passing through it will be 50mA
Explanation:
electric current = charge / time
I = Q / TI = 0.5 / 10 I = 0.05 amperecurrent = 0.05 A = 50mA
If 0.5C charge passes through a wire in 10 seconds, then 50mA current is flowing through the wire. Thus, the correct option is C.
What is Electric current?
Electric current is the flow of electricity in an electronic circuit. It is the amount of electricity flowing through a electronic circuit. It is generally measured in amperes (A). The larger the value in amperes, the more electricity is flowing in that circuit.
The formula for calculation of Electric current is:
I = Q/T
where, I = electric current,
Q = amount of charge,
T = time required
Therefore, the current flowing in the wire is:
I = 0.5C/ 10 seconds
I = 0.05 A or 50mA (1mA = 10⁻³A)
Therefore, the correct option is C.
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In the figure below, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm?
Answers
In the figure below, the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm is 63 m/s.
What is oscillation?Periodic or oscillatory motion is defined as a motion that repeats itself. Due to a restoring force or torque, an object in such motion oscillates around an equilibrium position.
Energy is conserved in oscillation.
So, the maximum loss in Potential Energy = Maximum gain in Kinetic energy
5 J - 1 J = Maximum gain in Kinetic energy
Maximum gain in Kinetic energy = 4 J
\(0.5 \times m \times vmax^2 = 4\\0.5 \times 2.0 \times 10^-3\; Kg \times vmax^2 = 4 J\\vmax^2 = 4 \times 10^3 m^2/s^2\\vmax = 63.2 m/s\)
Therefore, the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm is 63 m/s.
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A man is standing away from the School
Building at a distance of
300m . He claps his hands and hears an echo calculate the time interval of him hearing his echo
Answers
The time interval between the man clapping and hearing his echo is approximately 1.75 seconds.
What do you mean by echo?An echo is a repetition or reflection of a sound or signal. It can be caused by sound waves bouncing off a surface, signal interference, or the repetition of a message in communication.
The speed of sound in air at room temperature is approximately 343 meters per second. When a person claps, the sound waves propagate outward in all directions and reach the school building, where they bounce off and return to the person as an echo. The time it takes for the sound to travel the distance to the building and back to the person is the time interval between the clap and the echo.
To calculate the time interval, we can use the following formula:
time = distance / speed
where distance is the total distance traveled by the sound (twice the distance from the person to the school building), and speed is the speed of sound in air.
distance = 2 x 300m = 600m
speed = 343 m/s
time = 600m / 343 m/s = 1.75 seconds (rounded to two decimal places)
Therefore, the time interval between the man clapping and hearing his echo is approximately 1.75 seconds.
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One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted in newtons by a 0.200 mg chip of paint that strikes a spacecraft window at a relative speed of 3.00 ✕ 10^3 m/s and sticks, given the collision lasts 6.00 ✕ 10^−8 s. (Enter the magnitude.)
Answers
Given:
• Mass, m = 0.200 mg
,• Speed, v = 3.00 x 10³ m/s
,• Time, t = 6.00 x 10^⁻⁸ s.
Let's calculate the force exerted.
Using the inpulse-momentum theroerm, we have:
impulse = change in momemntum
Where:
Impulse = force x time
change in momentum = mass x velocity.
Thus, we have:
\(F\times6.00\times10^{-8}=(0.200\times10^{-6})\times(3.00\times10^3)\)Let's solve for the force F:
\(\begin{gathered} F=\frac{(0.200\times10^{-6})(3.00\times10^3)}{6.00\times10^{-8}} \\ \\ F=10000N \end{gathered}\)Therefore, the force exterted is 10000 N.
ANSWER:'
10000 N
what is the Vector product of A=2.00i+3.00j+1.00k and B= 1.00i -3.00j -2,00k
Answers
The vector product of A=2.00i+3.00j+1.00k and B=1.00i-3.00j-2.00k is C=9.00i+4.00j-9.00k.
To find the vector product (also known as the cross product) of two vectors, A and B, we can use the following formula:
C = A × B
Where C is the resultant vector, A and B are the given vectors, and × denotes the cross product.
Given A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k, we can substitute these values into the formula to find the vector product:
C = (2.00i + 3.00j + 1.00k) × (1.00i - 3.00j - 2.00k)
Now, let's expand the cross product using the properties of vector products:
C = (2.00i × 1.00i) + (2.00i × -3.00j) + (2.00i × -2.00k) +
(3.00j × 1.00i) + (3.00j × -3.00j) + (3.00j × -2.00k) +
(1.00k × 1.00i) + (1.00k × -3.00j) + (1.00k × -2.00k)
Now, let's calculate each of these cross products:
C = (2.00 × 1.00) \(i^2\) + (2.00 × -3.00) i × j + (2.00 × -2.00) i × k +
(3.00 × 1.00) j × i + (3.00 × -3.00) \(j^2\) + (3.00 × -2.00) j × k +
(1.00 × 1.00) k × i + (1.00 × -3.00) k × j + (1.00 × -2.00) \(k^2\)
Since i × j = k, j × k = i, and k × i = j, we can simplify the expression further:
C = 2.00k - 6.00i + 4.00i - 9.00j + k - 3.00j - 2.00j - 2.00k
Combining like terms, we get:
C = (2.00i + 4.00i) + (-6.00i - 9.00j - 3.00j) + (2.00k + k - 2.00k)
Simplifying further:
C = 6.00i - 12.00j + k
Therefore, the vector product of A and B is C = 6.00i - 12.00j + k, which can be written as C = 9.00i + 4.00j - 9.00k in terms of i, j, and k.
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The vector product of A and B is -3i - 5j - 9k.
Explanation:The vector product, also known as the cross product, of two vectors A and B is denoted as A x B. It is a vector that is perpendicular to both A and B. To calculate the vector product, you can use the formula A x B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k.
In this case, we have A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k. Substituting the values into the formula, we get A x B = (3 * -2 - 1 * -3)i + (1 * 1 - 2 * -2)j + (2 * -3 - 3 * 1)k = -3i - 5j - 9k.
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A 2 m long wire carrying 2 A of current pointing to the right is placed in a magnetic field of 4 T directed away from you. Which direction does the force on the wire point?
A. Down
B. Up
C. Left
D. Right
Answers
Explanation:
To determine the direction of the force on the wire, we can use the right-hand rule for the cross product of two vectors. The force on the wire is given by:F = I * L x Bwhere I is the current, L is the length of the wire, and B is the magnetic field.
If we point our right-hand thumb in the direction of the current (to the right), and our fingers in the direction of the magnetic field (away from us), then our palm will point in the direction of the force.
So, using the right-hand rule, we can see that the force on the wire will be directed downward. Therefore, the correct answer is A. Down.A 15 year old boy requires eyeglasses with lenses of 2 diopters power in order to read a book at 25 cm. Five years later he finds that while wearing the same glasses, he must hold a book 40 cm from his eyes. What power of lenses does he require at 20 years in order to read a book at 25 cm?
Answers
At 20 years old, the boy would require eyeglasses with lenses of approximately -1.49 diopters power in order to read a book at 25 cm.
How to solve for the power of lenses1/f1 = 1/v - 1/u1
1/f1 = 1/∞ - 1/0.25 (converting 25 cm to meters)
1/f1 = 0 - 4
1/f1 = -4
f1 = -1/4
f1 = -0.25 meters
The initial lens power (P1) is the reciprocal of the focal length:
P1 = 1/f1
P1 = 1/-0.25
P1 = -4 diopters
Now let's calculate the final focal length (f2) using the final distance (v2) of 40 cm:
1/f2 = 1/v2 - 1/u1
1/f2 = 1/0.40 - 1/0.25
1/f2 = 2.5 - 4
1/f2 = -1.5
f2 = -1/1.5
f2 = -0.67 meters
The final lens power (P2) is the reciprocal of the focal length:
P2 = 1/f2
P2 = 1/-0.67
P2 ≈ -1.49 diopters
Therefore, at 20 years old, the boy would require eyeglasses with lenses of approximately -1.49 diopters power in order to read a book at 25 cm.
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I need help answering these questions using my experiment results. I will send you the results
Answers
Answer:
(a) It changed
(b) It changed
(c) It changed
(d) It changed
Explanation:
For each parameter, we get:
(a) the final velocity of the ball.
The velocity is equal to the distance over time. Since the distance is always 10 m, the velocity will depend on the time. So, when the time is greater, the final velocity is smaller.
In this case, we can see that for each angle, we get different times, so, the angle affects the final velocity of the ball.
(b) work
The work can be calculated as:
W = Fdcosθ
Where F is the force, d is the distance and θ is the angle between them. When we change the angle of the incline, we affect the angle of the Force and the displacement, so the work changes.
(c) initial potential energy
The potential energy depends on the initial height, if the height is greater, the potential energy is greater. So, when the angle of the incline change, the height change, so the potential energy change
(d) final kinetic energy
The kinetic energy depends on the final velocity, if the final velocity is greater, the kinetic energy is greater. Since the final velocity changes with the angle, the kinetic energy also changes with the angle.
Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answers
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
What is the magnitude of the resultant vector? Round your answer to the nearest tenth. m
Answers
The magnitude of the resultant vector to round the answer to the nearest tenth, we look at the digit in the hundredth's place. If this digit is 5 or greater, we round up. If it is less than 5, we round down.
In the study of physics, we use vectors to represent quantities that have both direction and magnitude. It is often the case that we want to add two or more vectors together to obtain a single vector that represents the net result of these additions. The process of adding two or more vectors together is known as vector addition.The magnitude of the resultant vector is the length of the line that represents it on a scale drawing.
When we add two or more vectors together, the resultant vector is the vector that represents the net result of these additions. To find the magnitude of the resultant vector, we use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In the case of vector addition, the hypotenuse is the resultant vector, and the other two sides are the component vectors. If we have two vectors a and b, the magnitude of the resultant vector is given by the following equation:|R| = √(ax2 + bx2)where R is the resultant vector, a and b are the component vectors, and x is the angle between the vectors.
For example, if the answer is 12.345, we would round it to 12.3.
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A rigid body acted upon by a set of forces . The magnitude of the forces are as follows F1=3N,F2=6N,F3=3N,F4=4N,F5=3Nand F6=3N. Identify the couple among these forces
Answers
The forces F3 and F6 form a couple since they are parallel, act in the same directions, and have the same magnitude (both are 3N), but they do not have the same point of application.
A couple is a pair of equal but disjointed forces that act in opposite directions and along parallel lines of force.
The rigid body rotates about its center of mass as a result of the forces acting on it at various places.
We can observe that the forces F3 and F6 in the provided set of forces are parallel, have the same magnitude of 3N, and act in opposite directions.
However, because they are applied to various locations on the rigid body, the body will rotate as a result. The stiff body tends to rotate around its center of mass because of this phenomenon, which is known as a couple.
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Use the data table and below to answer
Answers
Using the CER, write an essay describing what might influence some teens to choose a sedentary lifestyle. 1. suggest ways to encourage these teens to become more physically active. 2. Use correct spelling and punctuation. Use no less than 8 sentences. *
Answers
Answer:
Sedentary lifestyle is the lifestyle by which most physical activity is abandoned, performing activities that do not require energy consumption or large muscle movements on a large scale, such as using a computer, driving a car or playing video games.
Today, most young people have gradually turned towards sedentary lifestyles, mainly motivated by the increase in technological availability, and the extensive dependence generated on technology both to communicate with their peers (cell phones, social networks, etc. .) and for leisure time (video games, etc.).
Some ways to promote physical activity in young people and prevent sedentary lifestyle can be to create sports groups, where young people can establish social relationships without depending on networks or technological devices, or establish tasks of physical activity during study or work hours.
If magnet A can pick up 3 steel paperclips and magnet B can pick up 5 paperclips, which one is stronger
Answers
Answer:4
Explanation:
The clips are not affected by magnet strength
How did earth change about 2.5 billion years ago when many organisms began using photosynthesis to make food
A. The amount of oxygen in the atmosphere increased
B. Mass extinctions occurred
C. The oceans became larger
D. Rainfall increased