Answer:
\(1200\ \text{N}\)
Explanation:
F = Force on the skier = 60 N
\(\mu\) = Coefficient of friction = 0.05
w = Weight of skier
Force is given by
\(F=\mu w\)
\(\Rightarrow w=\dfrac{F}{\mu}\)
\(\Rightarrow w=\dfrac{60}{0.05}=\dfrac{6000}{5}\)
\(\Rightarrow w=1200\ \text{N}\)
Weight of the skier on which the force is being applied is \(1200\ \text{N}\) .
Jesse drives 120km to a farm. His trip takes 2 1/2 hoursWhat is his speed?
Speed = distance / time
Speed = 120 km / 2 1/2 hours
Speed = 48 km per hour
Vocabulary Terms - Define the following terms
1. Scalar-
2. Vector-
3. Magnitude-
4.1 Vectors in Physics Worksheet
4. Vector Components-
Conceptual Questions
5. What distinguishes a vector from a scalar?
6. What does the magnitude of a vector refer to?
Four men are pushing on a broken car. One man pushes on the car with 345 N, another with 203 N, another
with 291 N and 101 N. The friction between the car and road pushes in the opposite direction with a force of 940 N.
1.) Make a claim: What is the net force on the car?
2.) Cite evidence: What evidence supports your claim?
3.) Make a claim: Will the car move?
4.) Provide reasoning: Why do you say that?
Answer:
1. 3 N
2. The total force being put on the car by the men is 943 while the friction is going in the opposite direction with a force of 940.
3. Yes
4. The net force is not equal to zero
Explanation:
1. 345 + 203 + 291 + 101 = 943 + -940 = 3
PLEASE HELP!!
Which statement accurately describes a balanced force?
A 2-N force presses down on the marble at the same time as a 1.5-N force presses up on the marble.
A marble rolling downhill suddenly comes to rest at a garden wall.
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
A marble resting on the sidewalk suddenly begins to roll downhill without being touched.
Answer:
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
Explanation:
just took test
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Balanced force is when the net force applied on the object is zero than said to be balanced.
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
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(Forces and the Laws of Motion pg. 141; Friction) (Problem 4)
A box of books weighing 325 N moves at a constant velocity across the
floor when the box is pushed with a force of 425 N exerted downward at an
angle of 35.2° below the horizontal. Find μk between the box and the floor.
The coefficient of kinetic friction is determined as 0.75.
What is coefficient of friction?
The coefficient of kinetic friction is calculated by applying the newton's second law of motion.
Fsinθ - Ff = ma
where;
Ff is frictional forceθ is angle of applied forceW = mg
where;
m is mass of the boxm = W/g
m = 325/9.8
m = 33.2 kg
425 sin(35.2) - Ff = 33.2a
425 sin(35.2) - μW = 33.2a
at constant velocity, a = 0
425 sin(35.2) - μW= 0
μW = 244.98
μ = 244.98/W
μ = 244.98/325
μ = 0.75
Thus, the coefficient of kinetic friction is 0.75.
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When the dried-up seed pod of a scotch broom plant bursts open, it shoots out a seed with an initial velocity of 2.65 m/s
at an angle of 30.0 ∘ below the horizontal. The seed pod is 0.460 m
above the ground.
How long does it take for the seed to land?
t= ? sec
What horizontal distance does it cover during its flight?
x=? M
Answer:
To solve this problem, you'll need to break the initial velocity of the seed into its horizontal and vertical components, then use the equations of motion to find the time of flight and horizontal distance.
The initial velocity (v) of the seed is 2.65 m/s. The angle it's launched at (θ) is 30.0 degrees below the horizontal. The height (h) it's launched from is 0.460 m.
First, calculate the horizontal (v_x) and vertical (v_y) components of the velocity. Because the seed is launched downward, the vertical component will be negative:
v_x = v * cos(θ) = 2.65 m/s * cos(30.0) = 2.29 m/s
v_y = v * sin(θ) = -2.65 m/s * sin(30.0) = -1.325 m/s
Next, use the equation of motion to find the time it takes for the seed to hit the ground:
h = v_y * t + 0.5 * g * t^2
Where g is the acceleration due to gravity, which is approximately 9.8 m/s². Solving the equation for t gives:
t = (-v_y - sqrt((v_y)^2 - 4 * 0.5 * g * (-h))) / (2 * 0.5 * g)
Plugging in the values:
t = (1.325 + sqrt((-1.325)^2 - 4 * 0.5 * 9.8 * (-0.460))) / (2 * 0.5 * 9.8)
t = 0.182 seconds
Finally, use the horizontal velocity and time of flight to find the horizontal distance the seed covers:
x = v_x * t = 2.29 m/s * 0.182 s = 0.417 m
So, the seed lands after approximately 0.182 seconds and travels approximately 0.417 meters horizontally.
What do the three dream theories all have in common?
Dream theories have in common that they are related to conceptions about reality.
What are dream theories?Dream theories are a series of theories that focus on explaining the dreams that an individual experiences when sleeping.
What theories of sleep exist?There are three main theories about dreams that are:
Activation-synthesis theory: This theory states that the brain is randomly activated during sleep and that brain activity is generally associated with memories and sensory information.
Theory of psychoanalysis: This theory states that dreams contain unconscious information for the individual about his interpretation of reality. This information is later synthesized and processed by reason so that the individual takes it as a meaningful message.
Threat Rehearsal Theory: This theory states that dreams are "rehearsals" of risk situations in which situations that are considered dangerous to the individual are simulated and in which the brain is trained to act in them.
What similarities do these theories have?The main similarity that these three theories have is that they are related to the interpretation that the individual has of his reality and the sensory information of his interaction with the environment.
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Equipotential Surfaces: A region of space contains a uniform electric field directed in the positive x direction as shown. Among the following the correct statements about the electric potential is: Select one: VYYc b. V₁ V₂ Ve d. We can't judge
The true statement about the electric potential for the equipotential surface is \(V_A = V_B = V_C\)
What is equipotential surface?A surface with an equipotential potential is one where all points on the surface have the same electric potential. .
That is an equipotential surface is that surface at every point of which, the electric potential is the same.
The formula for the potential across every point on the surface is given as;
V = F/Q x R
V = ER
where;
E is the electric field across the surfaceR is the distance or position of the chargeSince the surface is equipotential with uniform electric across the surface, the electric potential at any point across the surface will be the same.
So \(V_A = V_B = V_C\)
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For the microscope to be in focus, how far should the objective lens be from the specimen?
Answer:
p ≈ f_ objective Therefore for the object to be in focus it must be close to the focal length
Explanation:
A microscope is an optical instrument that uses two lenses, or a long focal length objective lens that forms a real image of the object and an eyepiece that forms a virtual image of the object. Therefore for the object to be in focus it must be close to the focal length
p ≈ f_ objective
p distance objetive
The greenhouse effect is
Can you help me with the blank part please I need it done today
Now the 30.0 kg crate sits on a frictionless inclined plane of 35.0*
0=35.0⁰
2
What is the magnitude of the normal force on the crate from the plane?
Answer:
..............
Explanation:
..............
Part 1
1. Consider the potential energy diagram shown below. This graph shows the chemical potential energy in a reaction system over time. The y–axis is potential energy in kilojoules. The x–axis is the reaction progress, or time.
a. Does this graph represent an endothermic or an exothermic reaction? Explain your answer.
b. What is the enthalpy change, ΔH, for this reaction? Show your work.
c. What is the activation energy, Ea, for this reaction? Show your work.
Part 2
2. In a particular chemical reaction, the energy of the reactants is 30 kJ and the energy of the products is 5 kJ. The maximum energy of the system is 40 kJ. Use this information to answer questions a – d.
a. Sketch a potential energy diagram for this reaction. Make sure to label the energy of the reactants, the energy of the products, the activation energy, and the enthalpy change for the reaction. (Note: You may use the graph provided below or sketch your own. Resize as needed.)
b. What is the activation energy for this reaction?
c. What is the enthalpy change for this reaction?
d. Is this reaction endothermic or exothermic? Explain your answer in two ways: first, using the energy values, and second, by referring to the shape of the graph.
Part 3
3. The coating on the head of a match is highly flammable. When it burns, it releases a great deal of energy. However, before the match can burn, it must gain a small amount of energy from a spark. That spark is typically produced by striking (rubbing) the match head against a rough surface.
a. Sketch a potential energy diagram that represents the striking and burning of the match. Remember to label the diagram with the energy changes that occur. (Note: you do not have to use actual energy values. And you may use the graph provided below or sketch your own.)
b. Describe a potential energy diagram that represents the striking and burning of the match.
1a) Energy is absorbed, and the reaction is endothermic.
1b) The products have higher potential energy, the enthalpy change is positive, indicating an endothermic reaction.
1c) The peak of the potential energy diagram.
2a) The activation energy labeled as the difference between the reactants and the peak
2b) The activation energy can be determined by calculating the difference between the reactants.
2c) The enthalpy change can be calculated by finding the difference between the energy of the reactants and the energy of the products.
2d) The reaction is exothermic. In terms of the graph's shape.
3a) A decrease in potential energy as the products form.
3b)This indicates that a small amount of energy from the spark is needed to overcome the activation energy barrier
Part 1:
1a. To determine if the reaction is endothermic or exothermic, we need to analyze the potential energy diagram. If the products have lower potential energy than the reactants, it indicates that energy is released, and the reaction is exothermic. Conversely, if the products have higher potential energy than the reactants, it suggests that energy is absorbed, and the reaction is endothermic.
1b. The enthalpy change (ΔH) for the reaction can be calculated by comparing the potential energy of the products and the reactants. If the products have lower potential energy, the enthalpy change is negative, indicating an exothermic reaction. If the products have higher potential energy, the enthalpy change is positive, indicating an endothermic reaction.
1c. The activation energy (Ea) can be determined by examining the energy difference between the reactants' potential energy and the peak of the potential energy diagram.
Part 2:
2a. Since the energy of the reactants is 30 kJ, the energy of the products is 5 kJ, and the maximum energy of the system is 40 kJ, we can sketch a potential energy diagram with the reactants at 30 kJ, the products at 5 kJ, the activation energy labeled as the difference between the reactants and the peak, and the enthalpy change as the difference between the reactants and products.
2b. The activation energy can be determined by calculating the difference between the reactants' energy and the peak of the potential energy diagram.
2c. The enthalpy change can be calculated by finding the difference between the energy of the reactants and the energy of the products.
2d. Based on the energy values, if the energy of the products is lower than the energy of the reactants, the reaction is exothermic. In terms of the graph's shape, if the potential energy decreases from reactants to products, it indicates an exothermic reaction.
Part 3:
3a. The potential energy diagram for the striking and burning of a match can be sketched to show the initial potential energy of the reactants, a peak representing the activation energy, and a decrease in potential energy as the products form.
3b. The potential energy diagram would show an initial higher potential energy for the reactants, a peak representing the activation energy required for the reaction to occur, and a decrease in potential energy as the products form. This indicates that a small amount of energy from the spark is needed to overcome the activation energy barrier, leading to the release of a greater amount of energy during the burning process.
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Food manufacturers create fats by adding hydrogen to fats?
True, Food manufacturers create fats by adding hydrogen to fats.
What is hydrogenation?Hydrogenation is used in the oil industry in making trans fats or margarine by increasing the melting point through reducing the carbon-to-carbon double bonds..
During hydrogenation, unsaturated fats undergo a chemical reaction in the presence of hydrogen gas and a catalyst, typically nickel.
The process involves the addition of hydrogen atoms to the carbon double bonds in the fatty acid molecules, resulting in the conversion of some of the double bonds into single bonds.
This reduces the number of unsaturated bonds in the fat, making it more saturated.
So we can conclude that the statement is true.
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When the skin produces hair, it is removing excess water and salts from the body.
True or false?
You leave a pastry in the refrigerator on a plate and ask your roommate to take it out before youget home so you can eat it at room temperature, the way you like it. Instead, your roommateplays video games for hours. When you return, you notice that the pastry is still cold, but thegame console has become hot. Annoyed, and knowing that the pastry will not be good if it ismicrowaved, you warm up the pastry by unplugging the console and putting it in a clean trashbag (which acts as a perfect calorimeter) with the pastry on the plate. After a while, you find thatthe equilibrium temperature is a nice, warmTeq.. You know that the game console has a mass ofm1. Approximate it as having a uniform initial temperature ofT1. The pastry has a mass ofm2and a specific heat ofc2, and is at a uniform initial temperature ofT2. The plate is at the sameinitial temperature and has a mass ofm3and a specific heat ofc3. What is the specific heat ofthe console
Answer:
\(c_{e1} = \frac{(m_2 c_{e2} \ + m_3 c_{e3} ) \ (T_{Teq} - T_2) }{m_1 (T_1 - T_{eq}) }\)
Explanation:
This is a calorimeter problem where the heat released by the console is equal to the heat absorbed by the cupcake and the plate.
Q_c = Q_{abs}
where the heat is given by the expression
Q = m c_e ΔT
m₁ c_{e1) (T₁-T_{eq}) = m₂ c_{e2} (T_{eq} -T₂) + m₃ c_{e3} (T_{eq}- T₁)
note that the temperature variations have been placed so that they have been positive
They ask us for the specific heat of the console
\(c_{e1} = \frac{(m_2 c_{e2} \ + m_3 c_{e3} ) \ (T_{Teq} - T_2) }{m_1 (T_1 - T_{eq}) }\)
Hydraulic systems utilize Bernoulli’s principle. T. F.
its FALSE
The answer is true, that the hydraulic press utilizes Bernoulli's principle.
It can be derived from the Principle of conservation of energy.
What is Bernoulli's Principle?According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy. The mathematical concept is named after Swiss mathematician Daniel Bernoulli, who first published it in his book Hydrodynamics in 1738.
The venturi tube is a real-world example of Bernoulli's Principle in action. The venturi tube has an air intake that constricts to a throat and an exit segment that widens as it moves backward. The entrance and outflow both have the same diameter.
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Matter can undergo chemical reactions which feature of the components only stays the same in chemical reactions
In chemical reactions, the total mass of the components remains the same.
Chemical reactions involve the transformation of substances into new substances with different chemical properties. During these reactions, various changes occur, such as the rearrangement of atoms, the breaking and forming of chemical bonds, and the conversion of reactants into products. However, one fundamental principle that remains constant is the law of conservation of mass.
The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction. This means that the total mass of the reactants must be equal to the total mass of the products. No matter can be lost or gained during the reaction; it simply undergoes a rearrangement at the atomic or molecular level.
This principle holds true regardless of the complexity of the chemical reaction. Whether it involves simple reactions between two elements or complex reactions with multiple reactants and products, the total mass before and after the reaction remains constant.
This concept is vital in understanding stoichiometry, which is the quantitative relationship between reactants and products in a chemical reaction. By balancing chemical equations and applying the law of conservation of mass, scientists can determine the relative amounts of substances involved in a reaction.
Overall, while the physical and chemical properties of substances may change during a chemical reaction, the total mass of the components involved in the reaction remains constant.
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A car drives 10km with a speed of 72 km/hr and then runs out of gas. Then you walk 2km for the next 30 min until you find a gas station. (A) What is the displacement of the total trip? (B) How long does the entire trip take? (C) What is the average velocity of the entire trip?
Answer:
(A) Total Displacement = 12 km
(B) t = 38.33 min
(C) Average Velocity = 18.8 km/h
Explanation:
(A)
The displacement of the trip is the sum of both distances:
Total Displacement = 10 km + 2 km
Total Displacement = 12 km
(B)
First we calculate the time taken by the car:
s = vt
where,
s = distance covered by car = 10 km
v = speed of car = 72 km/h
t = time taken = ?
Therefore,
t = (10 km)/(72 km/h)
t = (0.139 h)(60 min/1 h)
t = 8.33 min
now, we add the 40 min of walking in this:
t = 8.33 min + 30 min
t = 38.33 min
(C)
The average velocity is given as:
Average Velocity = Total Displacement/t = (12 km/38.33 min)(60 min/1 h)
Average Velocity = 18.8 km/h
Answer:
Explanation:
Answer:
(A) Total Displacement = 12 km
(B) t = 38.33 min
(C) Average Velocity = 18.8 km/h
Explanation:
(A)
The displacement of the trip is the sum of both distances:
Total Displacement = 10 km + 2 km
Total Displacement = 12 km
(B)
First we calculate the time taken by the car:
s = vt
where,
s = distance covered by car = 10 km
v = speed of car = 72 km/h
t = time taken = ?
Therefore,
t = (10 km)/(72 km/h)
t = (0.139 h)(60 min/1 h)
t = 8.33 min
now, we add the 40 min of walking in this:
t = 8.33 min + 30 min
t = 38.33 min
(C)
The average velocity is given as:
Average Velocity = Total Displacement/t = (12 km/38.33 min)(60 min/1 h)
Average Velocity = 18.8 km/h
What is acceleration
\({\tt{\red{\underline{\underline{\huge{Answer:}}}}}}\)
\(\longrightarrow\) The rate of change of velocity per unit time is called acceleration.
\(\longrightarrow\) Its SI unit is m/s².
\(\huge\boxed{\fcolorbox{blue}{red}{Thank you}} \)
When do rubber bands no longer act like springs?
Answer:
Rubbery materials act like simple springs when they're not deformed too much. Following the relation known as Hooke's law, a 10 percent increase in stretching force will make a typical rubber band 10 percent longer.
Explanation:
In Short when they become too deformed.
Answer:
yes
Explanation:
Rubbery materials act like simple springs when they're not deformed too much. Following the relation known as Hooke's law, a 10 percent increase in stretching force will make a typical rubber band 10 percent longer
correct me if im wrong
What is a lower fixed point in physics
In physics, a lower fixed point refers to the minimum temperature at which a particular substance or system can reach and below which it cannot be cooled further.
It is a fundamental concept in the study of thermodynamics, specifically in relation to phase transitions and the behavior of substances at low temperatures.
The lower fixed point is often associated with the concept of absolute zero, which is the lowest possible temperature in the Kelvin scale (-273.15 degrees Celsius or -459.67 degrees Fahrenheit).
At absolute zero, particles in a substance possess the minimum amount of energy and their motion ceases, resulting in the absence of thermal energy.
The lower fixed point serves as a reference point for temperature scales, such as the International Temperature Scale of 1990 (ITS-90), which defines temperature measurements based on fixed points like the melting point of certain substances and the triple point of water.
These fixed points provide reproducible and well-defined temperature values for calibration and measurement purposes.
Understanding the lower fixed point is crucial for various scientific and technological applications, such as cryogenics, superconductivity, and the study of quantum phenomena at extremely low temperatures.
By pushing the boundaries of cooling techniques, researchers aim to approach the lower fixed point and explore the fascinating properties and behaviors of matter at such extreme conditions.
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. A 5cm tall object is placed perpendicular to the principal axis of a convex lens of focal
length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position
and size of the image. Also find its magnification
The nature of the image formed by the convex lens is virtual, the position of the image is 30 cm away from the lens on the same side as the object, and the size of the image is twice the size of the object. The magnification is 2, meaning the image is magnified.
Given:
Object height (h) = 5 cm
Focal length of the convex lens (f) = 10 cm
Object distance (u) = 15 cm (positive since it's on the same side as the incident light)
To determine the nature, position, and size of the image, we can use the lens formula:
1/f = 1/v - 1/u
Substituting the given values:
1/10 = 1/v - 1/15
To simplify the equation, we find the common denominator:
3v - 2v = 2v/3
Simplifying further:
v = 30 cm
The image distance (v) is 30 cm. Since the image distance is positive, the image is formed on the opposite side of the lens from the object.
To find the magnification (M), we use the formula:
M = -v/u
Substituting the values:
M = -30 / 15 = -2
The magnification is -2, indicating that the image is inverted and twice the size of the object.
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In a DC generator, the generated emf is directly proportional to the
In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.
This relationship is described by the equation for the generated emf in a DC generator:
Emf = Φ * N * A * Z / 60
Where:
Emf is the generated electromotive force (in volts),
Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),
N is the number of turns in the armature winding,
A is the effective area of the armature coil (in square meters),
Z is the total number of armature conductors, and
60 is a constant representing the conversion from seconds to minutes.
From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.
The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.
The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.
Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.
By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.
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A lowest A on a piano has a frequency of 27.5 HZ if the tension in the 2.00m string is 308N and one half wavelength occupies the spring what is the mass of the wire
The mass of the wire of lowest A on a piano is 0.00165 kg.
The frequency of a vibrating string is given by the equation:
f = (1/2L) * sqrt(T/μ)
where f is the frequency of the string, L is the length of the string, T is the tension in the string, and μ is the linear mass density of the string (mass per unit length).
We know the frequency of the lowest A on a piano is 27.5 Hz. We also know that one half wavelength occupies the string, so the length of the string is half the wavelength:
L = (1/2) * λ
The wavelength of a sound wave is given by:
λ = 2L/n
where n is the number of nodes (points of zero displacement) in the wave. For the lowest A on a piano, n = 1, so we can write:
λ = 2L
Substituting this into the equation above for L, we obtain:
L = λ/2
Now we can substitute these values into the first equation:
27.5 = (1/2)(λ/2) * sqrt(308/μ)
Simplifying, we get:
λ = 4L
308/μ = 4(27.5)^2 (1/4)
μ = 0.000824 kg/m.
Since μ = m/L, where m is the mass of the wire and L is its length, we can find the mass of the wire by multiplying the linear mass density by the length of the string:
m = μL
The length of the string is given as 2.00 m, so we can write:
m = 0.000824 kg/m * 2.00 m = 0.00165 kg
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A 4.50-kg centrifuge takes 200 s to spin up from rest to its final angular speed with constant angular acceleration. A point P located 10.0 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full(final) speed. a) [4 points] What was its final angular speed
Answer:
Explanation:
ω = v / R
where ω is angular speed of a point situated at distance R from axis and having a linear speed of v .
Given v = 150 m/s ; R =.10 m
ω = 150 / .10
= 1500 radian /s .
Final angular speed is 1500 radian /s .
You perform an experiment to test how far a cannon will shoot a performer at
different angles. The data are shown below.
Angle
Distance (feet)
110
32°
36°
120
40°
128
440
133
48°
127
52
119
56°
109
60°
100
64°
91
68°
77
72°
63
At which angle will the performer travel the longest distance?
Answer:
44°
Explanation:
Look for the longest distance under the 'Distance ' column....look to the left to find the corresponding angle
Table clearly shows that the longest distance (133 ft) occurs at angle of 44°
name a substance which will undergo change E
Answer:
Water
Explanation:
At 0 degrees it's solid...Then it melts into a liquid and at 100 degrees it's gas Simple
What Health Related Component of Physical Fitness is the ability of the heart and lungs to supply oxygen to the body? a. Muscular Strength c. Cardiorespiratory Endurance b. Muscular Endurance d. Flexibility
The two masses (mA
= 6.50 kg is hanging and mB
= 3.30 kg is on the floor) in the Atwood's machine shown in the figure below are released from rest, with mA
at a height of 0.865 m above the floor. When mA
hits the ground its speed is 1.89 m/s. The pulley is not massless and can be considered a solid disk with a moment of inertia of (1/2)mpr2
.
What is the total mechanical energy of the two blocks prior to being released from rest?
(Figure 1)
What is the total mechanical energy of the two blocks when mA
hits the ground?
Part C
What is the rotational kinetic energy of the pulley just before mA
hits the ground?
Part D
What is the mass of the pulley?
A)The total mechanical energy of the two blocks prior to being released from rest can be found by adding the gravitational potential energy of mA and the pulley to zero.
B).The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J,where mp is the mass of the pulley.The total mechanical energy of the two blocks prior to being released from rest is54.33 J + 0 J = 54.33 J
C) The rotational kinetic energy of the pulley just before mA hits the ground is(0.178 mp) J.
D) The mass of the pulley ismp = (1/2)mpr²/R² =(1/2)(0.020 kg)(0.100 m)²/(0.200 m)² = 0.001 kg = 1 g.r = (1/2)R.
The Atwood's machine shown in Figure 1 consists of two masses mA = 6.50 kg and mB = 3.30 kg. The height of mA above the floor is 0.865 m. When mA hits the floor, its velocity is 1.89 m/s. The pulley has a moment of inertia (1/2)mpr². We have to find the total mechanical energy of the two blocks before they are released, the total mechanical energy when mA hits the ground, the rotational kinetic energy of the pulley just before mA hits the ground, and the mass of the pulley. Let's solve these one by one. Part A The total mechanical energy of the two blocks prior to being released from rest can be found by adding the gravitational potential energy of mA and the pulley to zero.
The equation for gravitational potential energy is mgh. The gravitational potential energy of mA and mB is mAg(h-hB)where h is the height of mA above the floor and hB is the height of mB above the floor. Since the pulley is at the same height as mB, its gravitational potential energy ismBg(h-hB).The gravitational potential energy of mA is6.50 kg × 9.81 m/s² × 0.865 m = 54.33 J.The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J,where mp is the mass of the pulley.The total mechanical energy of the two blocks prior to being released from rest is54.33 J + 0 J = 54.33 J.Part BThe total mechanical energy of the two blocks when mA hits the ground can be found by adding the kinetic energy of mA, the kinetic energy of mB, and the rotational kinetic energy of the pulley to the gravitational potential energy of mB and the pulley. The equation for kinetic energy is (1/2)mv². The kinetic energy of mA is(1/2) × 6.50 kg × (1.89 m/s)² = 11.54 J.The kinetic energy of mB is(1/2) × 3.30 kg × 0 m/s² = 0 J, since it is at rest.The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J.The rotational kinetic energy of the pulley is(1/2) × (1/2)mp × R² × ω²,where R is the radius of the pulley and ω is its angular velocity just before mA hits the ground. We can use the fact that the linear speed of the rope is the same on both sides of the pulley to find ω. The equation for linear speed is v = Rω. When mA hits the ground, its speed is 1.89 m/s. The speed of mB is zero. Since the rope is inextensible, the speed of the rope is also 1.89 m/s.
Therefore, the speed of the pulley is also 1.89 m/s. We can find the angular velocity of the pulley by dividing the linear velocity by the radius.ω = v/R = 1.89 m/s ÷ (0.200 m/2) = 18.9 rad/s.The rotational kinetic energy of the pulley is(1/2) × (1/2)mp × R² × ω² =(1/4)mpR²ω² =(1/4)mp(0.200 m)²(18.9 rad/s)² =(0.178 mp) J.The total mechanical energy of the two blocks when mA hits the ground is11.54 J + 0 J + 0 J + (0.178 mp) J = 11.72 J + (0.178 mp) J.Part CThe rotational kinetic energy of the pulley just before mA hits the ground is(0.178 mp) J.Part DWe can find the mass of the pulley by using the moment of inertia of a disk and the mass of the pulley. The moment of inertia of a disk is (1/2)mr². Therefore,(1/2)mpR² = (1/2)mpr²,where R is the radius of the pulley and r is the radius of gyration of the pulley. The radius of gyration of a disk is (1/2)R.
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