Physics midterm
Consider the two spheres, A and B, placed near each other. Each sphere has its own radius and the surfaces of the spheres are a distance d apart, as shown. If you are calculating the gravitational attraction between spheres A and B, what quantity would go in the denominator of Newton's law of universal gravitation?
(rA+d+rB)2
A weightlifter brings a 400-N barbell upward from his shoulders to a point 50 cm higher at a steady speed. During this process, what is the total work done on the barbell?
0 joules
A weightlifter exerts an upward force on a 1000-N barbell and holds it at a height of 1 meter for 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?
0 watts
The moon has a mass of 1×1022 kg, and the gravitational field strength at a distance R from the planet is 0.001 N/kg. What is the gravitational force exerted on the moon while it is in orbit around the planet?
1 X10up 19 N
The force of gravity on object A by object B is F. If the mass of object B was only half as large as it is, but everything else was kept the same, what would be the new force of gravity on object B by object A?
1/2F
The force of gravity on object B by object A is F. If the distance between the objects was tripled, but everything else was kept the same, what would be the new force of gravity on object B by object A?
1/9F
One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0 , as shown in Figure 1. When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0 , as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring's equilibrium position, as shown in Figure 3, where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible. When the object is located at the position shown in Figure 3, which of the following equations correctly indicates the total mechanical energy of the object-spring-Earth system?
12k0x20−mgx012k0x02−mgx0
A 5 kg block moves with a constant speed of 10 ms to the right on a smooth surface where frictional forces are considered to be negligible. It passes through a 2.0 m rough section of the surface where friction is not negligible, and the coefficient of kinetic friction between the block and the rough section μk is 0.2. What is the change in the kinetic energy of the block as it passes through the rough section?
20 J20 J of energy is removed from the block.
A moon of mass 1×1020 kg is in a circular orbit around a planet. The planet exerts a gravitational force of 2×1021 N on the moon. The centripetal acceleration of the moon is most nearly
20 m/S2
The force of gravity between object A and B is F. If the mass of object A was twice as large as it is, but if everything else was kept the same, what would be the new force of gravity between objects A and B?
2F
Two containers of water can have their individual masses varied by adding or removing water. The containers are initially a distance d apart, as measured from their centers, and are filled with water so that each has a mass M, as shown in Figure 1 above. The gravitational force that one container exerts on the other is F0. Water is then added to one container so that its mass increases to 1.5M, and water is removed from the other container so that its mass decreases to 0.5M, as shown in Figure 2. What is the new gravitational force exerted on one container by the other?
3/4F0
A weightlifter exerts an upward force on a 1000-N barbell and lifts the barbell 1 meter upward in 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?
500 watts
A 2 kg object is released from rest near the surface of a planet with a negligible atmosphere. A graph of the object's speed v as a function of time t is shown. What is the weight of the object on the planet?
8 N
Kepler's third law of planetary motion states that which two quantities are related?
A planet's orbital period and the size of the planet's orbit are related.
A scientist designs an experiment that requires two atomic particles whose only fundamental force exerted between them is the gravitational force. Which combination of particles and separation distance will meet this condition?
A proton and neutron located 1.0 mm apart
In which of the following situations is the gravitational force the dominant force?
A satellite is in orbit around a planet. and An object is in free fall just after it is released from rest
A block of mass M on an inclined surface is attached to a spring of negligible mass, as shown. The other end of the spring is attached to a wall, and there is negligible friction between the block and the incline. The block is pulled to a position such that the spring is stretched from its equilibrium position. The block is then released from rest. Which of the following systems can be classified as a closed system?
A system consisting of the block, spring, and Earth
According to Kepler's third law of planetary motion, if the Earth's orbit was twice as large as it is, how long would it take for the Earth to go around the Sun once?
About 2.8 times as long
A student must determine the inertial mass of a block attached to a horizontal track. The block is free to move horizontally along the track, as shown above. Frictional forces are considered to be negligible. The student may only choose two measuring tools to determine the inertial mass of the block. What tools should the student choose?
Accelerometer and Force sensor
A student performs an experiment in which an applied force is exerted on a 4kg object that is initially at rest. In the experiment, the applied force is exerted on the object until the object has moved a known distance. A motion detector measures the speed of the object after it has traveled the distance under consideration for a given trial. The table contains the data that were collected for three trials of the experiment. Which of the following conclusions can be drawn from the data? Select two answers.
Another external force must have done work on the object because the final kinetic energy of the object is less than the work done on the object by the applied force. The net work done on the object is the product of the applied force and the distance traveled for each trial.
In both figures, a particle of mass m is released from rest at a height, h. In figure (a), the particle is dropped straight downward and in figure (b) the particle is released from rest down a frictionless ramp. Which particle, the one in figure (a) or (b), will have more kinetic energy at the bottom?
Both particles will have the same kinetic energy at the bottom.
A block of mass 3kg on a horizontal surface travels at 6m/s toward the free end of a horizontal spring of negligible mass and spring constant k=200N/m , as shown in the figure. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. The block comes into contact with the free end of the spring such that the block remains fixed to the spring as the spring is compressed. A graph of the kinetic energy of the block as a function of the distance the spring is compressed is shown that was collected from experimental data. Which of the following data tables could best represent the spring potential energy of the block-spring system as a function of the distance that the spring is compressed?
Distance Spring Is Compressed (m)(m)Spring Potential Energy (J)(J)0.00.0000.30.3990.60.63636
Two experiments are conducted are conducted to determine the mass of an object. In Experiment 1, the object's weight is measured by using an electronic balance once the object has been placed at rest on the balance. In Experiment 2, the object is pulled along a horizontal surface with a spring scale such that the force reading on the spring scale remains constant while a motion detector is used to measure the instantaneous speed of the object as it is pulled. All frictional forces for both experiments are considered to be negligible. Which of the two experiments, if either, could be used to determine the gravitational mass of the object?
Experiment 1 only
One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0 , as shown in Figure 1. When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0 , as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring's equilibrium position, as shown in Figure 3, where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible.
F0x02F0x02
Planet X has a mass of M and a radius of R. Planet Y has a mass of 3M and a radius of 3R. Identical satellites orbit both planets at a distance R above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible.
Fy=1/3Fx
Which of the following forces is considered a conservative force?
Gravity
A block of mass M is placed on a semicircular track and released from rest at point P, which is at vertical height H1 above the track's lowest point. The surfaces of the track and block are considered to be rough such that a coefficient of friction exists between the track and the block. The block slides to a vertical height H2 on the other side of the track. How does H2 compare to H1?
H2<H1
One end of a vertical spring is attached to the ground with the other end above the ground such that the spring is at its equilibrium position. The spring has negligible mass and a spring constant k0 , as shown in Figure 1. When an object of mass m0 is released from rest above the spring, the object falls and then makes contact with the top of the spring with a speed v0 , as shown in Figure 2. The spring then compresses such that the object reaches a position x0 below the spring's equilibrium position, as shown in Figure 3, where the object comes to rest. The object is then directed upward by the spring until it is no longer in contact with the spring. The object then continues upward. The object-spring-Earth system has zero gravitational potential energy at the instant shown in Figure 2. All frictional forces are considered to be negligible. Which of the following describes the total mechanical energy of the object-Earth system during the time in which the object is in the air and the time in which the object is in contact with the spring? Assume all frictional forces are considered to be negligible.
In Air- CONSTANT Contact with Spring- not constant
A roller coaster track at a park includes a loop of radius R. A cart of mass M is located at the peak of the track, which has a height of 4R. The cart is subsequently released from rest such that it can slide down the track and go around the loop, as shown in the figure above. All frictional forces are considered to be negligible. Which of the following expressions for the cart's initial and final kinetic energy KE and the cart-Earth system's initial and final gravitational potential energy Ug could be used to determine the speed vf of the cart when it reaches the top of the loop?
Initial EnergyFinal EnergyUg0=4MgRUg0=4MgR KE0=0KE0=0Ugf=2MgRUgf=2MgR KEf=12mv2fKEf=12mv2f
A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. Consider the trial with the 45° ramp. Suppose the block is launched up the ramp such that it comes to rest at point B and then travels down the ramp. Which of the following best describes the block's kinetic energy KA when it reaches point A at the bottom of the ramp in comparison to the initial kinetic energy K0 before it travels up the ramp?
KA<K0KA<K0 , because the force of friction removes mechanical energy from the block-ramp-Earth system on its way up the ramp and back down the ramp.
Currently, the Moon takes 27.3 days to go around the Earth. Suppose a supervillain shifted the Moon into a new, lower, circular orbit. How long would it take for the Moon to go around the Earth in its new circular orbit?
Less than 27.3 days.
A rocket on Earth experiences an upward applied force from its thrusters. As a result of this force, the rocket accelerates upward at 2 m/s2. Assume that there are no other upward forces exerted on the rocket and that wind resistance is negligible. Which of the following combinations of the rocket's mass mRocket and force from its thrusters FThrusters would result in an upward acceleration of 2 m/s2? Select two answers.
M Rocket | 1kg and F thrusters | 12N
An Atwood machine is placed on a planet in which the acceleration due to gravity on the planet is unknown. Both ends of a light string are attached to two blocks such that M1>M2 , and the string passes through a pulley such that frictional forces are considered to be negligible, as shown above. The same tension force T is exerted on both blocks, and the block of mass M1 experiences an acceleration a0 in the downward direction when released from rest. Which quantities would allow the acceleration due to gravity on the planet to be determined?
M1. m2, and a0
A planet orbits a star along an elliptical path, as shown in the figure. Consider the system consisting of the planet and the star. How do the magnitude of the force exerted on the planet by the star and the total mechanical energy of the system change as the planet moves from point X to point Y?
Magnitude of Force Exerted on Planet by StarTotal Mechanical Energy of Planet and StarIncreasesRemains constant
Which of the following is an important difference between an object's mass and its weight?
Mass and weight have different units.
A block of mass M slides with speed v0 at the bottom of a ramp of negligible friction that has a height H, as shown. How do the total mechanical energy of the block alone and the total mechanical energy of the block-Earth system change when the block slides up the ramp to point P?
Mechanical Energy of Block Mechanical Energy of Block-Earth System Decreases Remains constant
Student X ties one end of a string to a 0.5 kg ball and swings the ball in a vertical circle of radius 1 m, as shown in the figure. Student Y uses video analysis to determine the speed of the ball at points A, B, C, and D, as shown in the table. Student X states that the data are incorrect because the tension in the string provides a centripetal force that should cause the ball to travel with a constant tangential speed. Is Student X's reasoning correct, and why or why not?
No, because the net centripetal force exerted on the ball is the combination of the tension force from the string and the force due to gravity from Earth.
A communications company requests that their satellite be placed 100,000 meters above the Earth's surface and then launched so that it moves in a geosynchronous orbit (meaning an orbit that takes exactly 24 hours to complete). Is this possible?
No, orbiting every 24 hours only happens at one specific orbital distance.
A toy car has an initial acceleration of 2m/s2 across a horizontal surface after it is released from rest. After the car travels for a time t=5 seconds, the speed of the car is 25m/s. Is the system consisting of only the car an open system or a closed system, and why?
Open system, because an external force is applied to the car that causes it to accelerate.
A student performs an experiment in which a ball travels in a perfect circle. The ball is attached to a string and travels in the horizontal, circular path, as shown in Figure 1. At time t0, the ball has a speed ν0. During the time interval of 0s to 2s, the force of tension in the string is recorded and graphed, as shown in Figure 2. Is the system consisting of the ball, string, and student an open system or closed system, and why?
Open system, because the force due to gravity from Earth is an external force that is exerted on the ball-string-student system
An object is placed on a rotating disk. The amount of time it takes the object to make one revolution around the center of the circle may be set at a known value. Which of the following procedures could be used to make the necessary measurements to find the coefficient of static friction between the object and the disk's surface?
Place the object on the disk and measure the distance from the center of the disk to the center of mass of the object by using a meter stick. Slowly increase the rate the disk rotates until the object begins to slide off the disk. Record the time in which the object makes one revolution around the center of the disk.
A rock of mass M is thrown from the edge of a cliff of height h with an initial velocity v0 at an angle θ with the horizontal, as shown in the figure. Point P is the highest point in the rock's trajectory, and point Q is level with the initial position of the rock. All frictional forces are considered to be negligible. Which of the following could correctly describe the total energy of the rock-Earth system at points P and Q?
PointP PointQ Mgh+12Mv20Mgh+12Mv02Mgh+12Mv20Mgh+12Mv02
Exoplanets (planets outside our solar system) are an active area of modern research. Suppose astronomers find such a planet that has the same mass as Earth, but has a radius that is about 10% less. Roughly, what acceleration due to gravity would you expect if you were standing on the surface of this new planet?
Roughly 12 m/s2
Exoplanets (planets outside our solar system) are an active area of modern research. Suppose astronomers find such a planet that has the same mass as Earth, but has a radius that is about 10% less. Roughly, what acceleration due to gravity would you expect if you were standing on the surface of this new planet?
Roughly 9 m/s2
If every object is attracted to every other object in the universe via gravity, why is it that you feel only one force of gravity on a day-to-day basis (the one from Earth)?
The Earth is big enough and close enough to cause a noticeable effect.
Kepler's first law of planetary motion tells us that planets move in ellipses. If we picture the elliptical orbit of a planet orbiting the Sun, where does the Sun fit into the picture?
The Sun is at one focus of the ellipse, with nothing at the other focus.
A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following systems does the total mechanical energy of the system remain constant?
The closed system containing the planet and the star
A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction to compress the spring and then release the block, what happens to the energy in the system immediately after the block is released?
The elastic potential energy in the spring decreases while the kinetic energy of the block increases.
Suppose you are floating in deep space (in a space suit). You grab onto two identical toolboxes, one of which is full of metal tools and the other of which is empty. As you shake the two tool boxes around by their handles, which is the correct statement about what you would notice?
The empty toolbox has a much smaller mass, so it is much easier to move it around.
Which of the following forces is considered a conservative force?
The force due to a spring
When helping a friend move into a new home, you push a chair across the room. What do you know about the force of gravity applied to the chair?
The force of gravity applied to the chair does not change the energy of the system (the chair) and therefore does no work on the system.
When helping a friend move into a new home, you push a chair across the room. What do you know about the force that you exert on the chair?
The force you exert on the chair contributes to the overall change in kinetic energy of the system (the chair) with a positive amount and therefore does positive work on the system.
When helping a friend move into a new home, you push a chair across the room. What do you know about the force of friction applied to the chair by the floor?
The frictional force applied to the chair contributes to the overall change in kinetic energy of the system (the chair) with a negative amount and therefore does negative work on the system.
A block slides along a rough surface and comes to a stop. What can you conclude about the frictional force exerted on the block?
The frictional force does negative work on the block and decreases its kinetic energy.
Newton's law of universal gravitation states that the force of gravity between you and the Earth gets smaller when you get further away from the center of the Earth. Why is it that we use the same acceleration due to gravity (g = 9.8 m/s2) for all physics problems without paying attention to whether the problem takes place at sea level or at the top of a tall mountain?
The height of a tall mountain is a tiny amount when compared to the radius of the Earth. So even going to the top of a tall mountain barely changes your distance to the center of the Earth.
Objects X and Y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, creating an Atwood's machine, as shown in the figure. The objects are initially at rest, and the mass of object Y is greater than the mass of object X. As object Y falls, how does the kinetic energy of the center of mass of the two-object system change? Justify your selection. All frictional forces are considered to be negligible.
The kinetic energy increases because the gravitational force due to Earth does positive net work on the system.
On a clear night you look up at the Moon overhead. At that moment the Moon is pulling on you via gravity with a certain amount of force, . Considering only magnitudes, how does the force you exert on the Moon via gravity compare to ?
The magnitude of the force you exert on the Moon is equal to .
Objects A and B are near each other in space and isolated from all other influences. Object A has a mass of 6m while object B has a mass of 2m. How does the magnitude of the net force on each object compare?
The magnitude of the net force on each object is the same.
A small block of mass M=0.10 kg is released from rest at point 1 at a height H=1.8 m above the bottom of a track, as shown in the diagram. It slides down the track and around the inside of a loop of radius R=0.6 m. The speed of the block is 2.5 m/s at point 3. Which of the following claims about the situation is correct?
The mechanical energy of the block-Earth system at point 3 is less than the mechanical energy of the block-Earth system at point 1.
If a planet is orbiting a star, what is the most accurate way to describe the shape of the orbit?
The orbit is shaped like an ellipse.
In both figures, a particle of mass m, is released from rest at a height, h. In figure (a), the particle is dropped straight downward and in figure (b) the particle is released from rest and slides down a ramp with a rough surface. Which particle, the one in figure (a) or (b), will have more kinetic energy at the bottom?
The particle in figure (a) will have more kinetic energy than the particle in figure (b) at the bottom.
In figure (b), a particle of mass m is released from rest at the top of a frictionless ramp of height h and in figure (c), a particle of mass 2m is released from rest at the top of the same frictionless ramp. Which particle, the one in figure (b) or (c), will have more kinetic energy at the bottom?
The particle in figure (c) will have more kinetic energy than the particle in figure (b) at the bottom.
If gravity attracts every object in the universe to every other object in the universe, why don't you feel a gravitational pull on you from other people as you walk past them?
The people walking past you do exert a gravitational force on you, but it is far too small to physically sense.
A ball of mass M is attached to a string of negligible mass that has a length R. The ball moves clockwise in a vertical circle, as shown above. Which of the following is true about the ball-string-Earth system as the ball moves from point 1 to point 2?
The potential energy decreases by 2MgR2MgR and the tension in the string increases by more than 2Mg2Mg.
A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the potential energy stored in the spring during this motion?
The potential energy in the spring increases because the spring does negative work on the block.
A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the work done by the spring on the block during this motion?
The spring does negative work on the block because the spring force is in the opposite direction of the block's displacement.
A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. The block can be pushed in the negative x-direction to compress the spring or pulled in the positive x-direction to stretch the spring. Where along the x-axis does the block have to be for the spring to have zero potential energy?
The spring has zero potential energy when the block is at x = 0, where the spring is neither stretched nor compressed.
A 5 kg object near Earth's surface is released from rest such that it falls a distance of 10 m. After the object falls 10 m, it has a speed of 12 m/s. Which of the following correctly identifies whether the object-Earth system is open or closed and describes the net external force?
The system is open, and the net external force is nonzero.
The total mechanical energy of a system as a function of time is shown in the graph. Which of the following statements is true regarding the system?
The system should be classified as an open system because mechanical energy can be added and removed from the system.
What is true about the work done by a conservative force?
The work done by a conservative force is always path independent.
What is true about the work done by a non-conservative force?
The work done by a non-conservative force will always change the total mechanical energy of a system.
The graph shows the x-component of a force applied to an object versus the position of that object in the x-direction. How is the work done by this force determined from the data in this graph?
The work done by the force is equal to the area under the force versus position function.
When you lift a book upward off of a table, what is true about the work done on the book by the force of gravity?
The work done by the force of gravity is negative and proportional to the upward displacement of the book.
An experiment is conducted such that an applied force is exerted on an object as it travels across a horizontal surface with a constant speed. A graph of the net force exerted on the object as a function of the object's distance traveled is shown. Which of the following claims is correct regarding the work done on the object by the applied force from one data point to the next data point?
The work done remains nearly constant for all displacements.
A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure. Astronomers making careful observations of the moon's orbit discover that the orbit is not perfectly circular, nor is it elliptical. Which of the following statements supports this observation?
There is another celestial body that exerts a gravitational force on the moon.
You observe two identical balls of putty heading directly toward each other at equal speeds. What can you say about their total kinetic energy?
They have twice the kinetic energy of either ball by itself.
Exoplanets (planets outside our solar system) are an active area of modern research. Suppose you read an article stating that there is a newly discovered planetary system with three planets. The article states that the outermost planet (Planet C) goes all the way around its star in less time than the innermost planet (Planet A). According to Kepler's laws of planetary motion, is this possible?
This is not possible, since it would violate Kepler's third law of planetary motion.
In which of these processes is the total energy of the system conserved?
Two balls of putty (the system) collide in midair and stick together.
A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. Consider the trial in which the ramp is at a 20° angle with the horizontal. The surface of the ramp has been replaced with a surface in which frictional forces are considered to be negligible. If the mass of the block is doubled and the initial launch speed is doubled, how could the student predict the new vertical of the block at point B?
Use 12mv2initial=mgyfinal12mvinitial2=mgyfinal to solve for yfyf.
A student must determine the effect of friction on the mechanical energy of a small block as it slides up a ramp. The block is launched with an initial speed v0 from point A along a horizontal surface of negligible friction. It then slides up a ramp, where friction is not negligible, that is inclined at angle θ with respect to the horizontal, as shown in the figure. The student measures the maximum vertical height h attained by the block while on the ramp, labeled as point B in the figure. At point B, the block comes to rest. The student performs three trials with the ramp at different angles, launching the block at the same initial speed v0 for each trial. The results from the trials are displayed in the table. How should the student use the data collected and the known quantities from the experiment to determine the total mechanical energy of the block-ramp-Earth system for all trials in the experiment?
Use K=12mv2K=12mv2 with the block's initial speed for one trial because the initial speed is the same in all trials.
A student must determine the work done on an object when an external force is exerted on it after it travels a specific distance. An external force F is exerted on an object at position x = 0 by a string as the object moves a distance D across a horizontal surface for a time tf . The force changes such that it decreases as the object moves. Which procedure could be used to determine the work done on the object by the external force?
Use a spring scale that is tied to the free end of the string and a meterstick to measure the force exerted on the object and the corresponding position for several positions until the object travels a distance DD . Graph the force on the vertical axis and the position on the horizontal axis. Determine the area bound by the curve and the horizontal axis.
A student uses a motion detector to record the speed of a 2kg object as a function of time as it travels across a horizontal surface of negligible friction. Data from the experiment are shown in the graph. In addition to the known mass, how can a student use the graph to determine the work done on the object from 0s to 5s ?
Use ΔK=12mΔv2ΔK=12mΔv2 with v0v0 equal to the speed of the object at 0s0s and vfvf equal to the speed of the object at 5s5s.
A variety of forces are applied to an object such that the net force does positive work on that object. What can you conclude about the speed of the object?
When the total work done on the object is positive, the object's speed will increase.
A block on a rough, horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall. The spring is compressed such that the block is located at position X. When the block-spring system is released, the block travels to the right through position Y and continues to travel to the right through position Z. Free body diagrams for the block at positions X, Y, and Z are shown in the figure. At which position does the block have the greatest kinetic energy?
Y
If you kick a big rock very hard while on the Earth, you might break a toe. If you kicked a similar rock while on the Moon, would you still be in danger of breaking your toe?
Yes, this is about the rock's mass, which is the same on the Moon as on the Earth.
A student analyzes data of the motion of a planet as it orbits a star that is in deep space. The orbit of the planet is considered to be stable and does not change over time. The student claims, "The only experimentally measurable external force exerted on the planet is the force due to gravity from the star." Is the student's claim supported by the evidence? What reasoning either supports or contradicts the student's claim?
Yes. Other external forces are exerted on the planet, but they are of negligible magnitude.
Satellite A orbits a planet at a distance d from the planet's center with a centripetal acceleration a0. A second identical satellite B orbits the same planet at a distance 2d from the planet's center with centripetal acceleration ab. What is the centripetal acceleration ab in terms of a0 ?
a0/4
A student must perform an experiment to determine the work done by a spring as it launches a block across a horizontal surface. The spring is initially compressed and the block is initially held at rest. After the spring is uncompressed, the block is no longer in contact with the spring. The spring constant is unknown, and the student may not use the mass or weight of the block in the experiment for any calculation. Which of the following measuring tools, when used together, can be used to determine the work done by the spring on the block? Select two answers.
force sensor meterstick
A small object of mass M is shot horizontally from a spring launcher that is attached to a table. All frictional forces are considered to be negligible. The ball strikes the ground a distance D from the base of the table, as shown in the figure. A second object of mass M2 is launched from the same launcher such that the spring is compressed the same distance as in the original scenario. The distance from the base of the table that the object lands is
greater than DD but less than 2D
The force exerted by our Sun on the planets in our solar system ______.
is proportional to the mass of the Sun.
In general, when a planet orbits a star, ______.
it moves with a higher speed during some parts of its orbit and a slower speed during other parts.
A student must conduct two experiments so that the inertial mass and gravitational mass of the same object can be determined. In the experiment to find the object's gravitational mass, the student ties one end of a string around the object with the other end tied to a spring scale so that the object can vertically hang at rest. In the experiment to find the object's inertial mass, the student uses a spring scale to pull the object, starting from rest, across a horizontal surface with a constant applied force such that frictional forces are considered to be negligible. In addition to the spring scale, the student has access to other measuring devices commonly found in a science laboratory. Which of the following lists the essential measuring devices the student can use to collect the data necessary to find the object's gravitational and inertial mass?
meter stick and timer
A block of mass M is held at rest on an inclined ramp that makes an angle θ with the horizontal, as shown in Figure 1. When released, the block slides down the incline and comes into contact with an uncompressed spring with spring constant k0 . The block slides an additional distance x0 before it compresses the spring a maximum distance, as shown in Figure 2. A student wants to use the law of conservation of energy to analyze the energies associated with the block-ramp-spring-Earth system. Which of the following equations should the student use to analyze the specific forms of energy in the system from the instant the block is released to the instant that the spring is at its maximum compression? Select two answers.
mg(y0−yf)=12kx20mg(y0−yf)=12kx02 , because the initial gravitational potential energy of the system is converted into spring potential energy. mgy0=mgyf+12kx20mgy0=mgyf+12kx02 , because some of the initial gravitational potential energy of the system is converted into spring potential energy.
The mechanical energy of a system is conserved during a certain process only if __________.
non-conservative forces do zero total work on the system during that process
Kepler's second law of planetary motion describes the area "swept out" by the line connecting a planet and the Sun during equal time intervals. The conceptual message of the law is that ______.
planets move faster when they are near the Sun, and move more slowly when they are farther away.
If Quantity X is conserved for a certain system and during a certain process, that means__________.
quantity X for that system does not change in any way during that process
A block is initially sliding along a surface of negligible friction with a speed v0. A constant force F0 is then exerted on the block. Which of the following figures represents the situations in which the kinetic energy of the block will initially decrease? Select two answers.
rectangle with top left diagonal F0 and bottom left diagonal F0
A ball of Mass M is swung in a vertical circle with a constant tangential speed. Figure 1 shows the forces exerted on the ball at the top of the circle, and Figure 2 shows the forces exerted on the ball at the bottom of the circle. Which of the following is an expression for the centripetal acceleration of the ball in terms of M, T1, T2, and any fundamental constants?
t1=t2/2M
A cart of mass M travels from point A at height h1 above the ground to point B on a track that is at a height h2, as shown in the figure. The speed of the cart at point A is nearly zero, and the frictional forces between the wheels, cart, and track are considered to be negligible. Which of the following graphs could represent the potential energy of the cart-Earth system at point A and point B? Select two answers.
the chart with B nothing and the chart with mainly A
