AP Physics Final
A student must design an experiment to determine the acceleration of a cart that rolls down a small incline after it is released from rest. The student has access to a timer, a meterstick, and a slow-motion camera that takes a photograph every 1/60 of a second. The angle that the incline makes with the horizontal is unknown, and the length of the incline is unknown. Which of the following procedures could the student use to determine the cart's acceleration? Select two answers.
- Use the timer to record the time it takes the cart to travel alongside a meter stick that is attached to the incline - use the slow-motion camera to film the cart as it rolls down the incline alongside a meter stick that is attached to the incline Explanations: - The meterstick can be used as the total distance the cart travels. The timer can be used to determine the time in which the cart travels the distance of the meterstick. If position is graphed as a function of time squared, the acceleration can be determined from the slope. - The time in which a photograph is taken after a previous photograph is known. If the cart travels alongside a meter stick, position and time data for the cart can be collected as it travels down the incline. If position is graphed as a function of time squared, the acceleration can be determined from the slope.
The table shows the vertical position as a function of time for an object that is dropped from a height of 5 m. A student must determine the acceleration of the object. Which of the following procedures could the student use to make the determination? Justify your selections. Select two answers.
- Use y=y0+vy0t+12ayt2, since all quantities are known except for the acceleration due to gravity. - Create a position-versus-time graph of the ball's motion, and use the data to create a velocity-versus-time graph of the ball's motion, since the slope of the velocity-versus-time graph represents the acceleration. explanations: - This method represents an algebraic approach for determining the acceleration of an object. The motion sensor measures the initial height of the ball, the final height of the ball, and the total time in which the ball was in the air. Since the initial speed of the ball is zero because it was released from rest, all quantities are known to use this equation. - This method represents a graphical approach for determining the acceleration of an object. Since the slope of a velocity-versus-time graph represents the change in velocity per unit of time of an object, the slope of a velocity-versus-time graph represents the acceleration of the object under consideration.
An object is held at an unknown height above Earth's surface, where the acceleration due to gravity of the object is considered to be constant. After the object is released from rest, a student must determine the object's speed the instant the object makes contact with the ground. Which of the following equations could the student use to determine the object's speed by using the fewest measuring tools if the student does not have access to a motion sensor? Select two answers.
- Vx= Vzo + axt - V^2x= V^2xo + 2a (x-xo) Explanations: - Without a motion sensor, the student would only need one stopwatch to use this equation to find the speed of the object at the instant it makes contact with the ground. - Without a motion sensor, the student would only need one meterstick to use this equation to find the speed of the object at the instant it makes contact with the ground.
An object is released from rest near a planet's surface. A graph of the acceleration as a function of time for the object is shown for the 4 s after the object is released. The positive direction is considered to be upward. What is the displacement of the object after 2s.
-10 m
An object is sliding to the right along a straight line on a horizontal surface. The graph shows the object's velocity as a function of time. What is the object's displacement during the time depicted in the graph?
0 m
A ball is thrown with an initial speed of 20 m/s at an upward angle of 60 ot the ground. If air resistance is negligible, what is the ball's speed at the instant it reaches its maximum height from the ground?
10 m/s
Block A is placed on a rough surface inclined at an angle θ above the horizontal. A taut string connects block A over a pulley to block B, which hangs from the string, as shown below. The masses of blocks A and B are MA and MB, respectively. At time t=0, block A is sliding up the slope as block B falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible. If the mass of block B is 2kg, the gravitational force exerted on block BB is most nearly which of the following?
20N - The gravitational force is the product of mass and the acceleration due to gravity. 2kg times 10N/kg gives a force of 20N.
Identical objects, Object X and Object Y, are tied together by a string and placed at rest on an incline, as shown in the figure. The distance between the center of mass of each object is 2m. The system of the two objects is released from rest, and a graph of the system's center of mass velocity as a function of time is shown. Based on the data, approximately how much time will it take the center of mass of Object X to reach point J near the bottom of the incline?
3.0 s
A ball traveling at a speed ν0 rolls off a desk and lands at a horizontal distance x0 away from the desk, as shown in the figure. The ball is then rolled off of the same desk at a speed of 3 v03. At what horizontal distance will the ball land from the table?
3xo - The horizontal distance can be determined by applying the following kinematic equation: x= xo+voxt+ 1/2 axt^2. In both situations, the initial position of the ball can be considered as zero, and the ball does not experience a horizontal acceleration. Since the ball's height above the ground remains constant in both situations, the time it takes for the ball to hit the ground will be the same in both situations. Therefore, the following relationship can be concluded: x-vox. Therefore, if the initial speed of the ball is increased by a factor of 3, then the horizontal distance traveled by the ball should be increased by a factor of 3.
A student drops a rock from rest at a distance h above the ground such that the rock hits the ground at time t0t0. At what distance above the ground should the rock be dropped such that it hits the ground at a time 2t0 after it is released from rest?
4h
A car goes from rest to 30 m's in 12 s with constant acceleration. How long does it take the car to go from rest to 15 m/s with the same acceleration?
6.0
A 5kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. After 2 s, the object has fallen 30 m. Air resistance is considered to be negligible. What is the gravitational force exerted on the 5 kg object near the planet's surface?
75 N - The kinematics equation that relates distance, time, and acceleration is used to calculate the acceleration of the object as it falls near the planet's surface: x=x0+vx0t+12axt2∴a=2xt2=2(7.5m)(1s)2=15 m/s2 Using the acceleration, the equation for weight can be used to calculate the weight of the 5 kg object: ΣF⃗ =ma=(5kg)(15m/s2)=75
Car X and car Y travel on a horizontal surface along different parallel, straight paths. Each car's velocity as a function of time is shown in the graph. Which of the following claims is correct about car X and car Y?
Both car X and car Y travel in the same direction - When a graph shows the velocity as a function of time for a moving object, the slope of the curve between two points in time represents the change in velocity per unit of time of the object. The change in velocity per unit of time for car X is represented by a positive slope. The change in velocity per unit of time for car Y is represented by a negative slope. The sign of the slope for each curve indicates the direction of the acceleration for the respective cars. However, at all points in time in this particular situation, the velocity for each car is either zero or positive. Therefore, both cars, at any given time, are either at rest or travel in the positive direction.
An object is thrown with an initial speed u near the surface of Earth. Assume air resistance is negligible and the gravitational field is constant. If the object is thrown horizontally, the direction and magnitude of its acceleration while it is the air is
Downward and constant
A student uses a motion sensor to collect data of the velocity of an object as a function of time during two experimental trials, as shown. In which trial does the object have the greatest magnitude of acceleration, and in which trial does the object travel the greatest distance?
Greatest Magnitude of acceleration- trial 2 greatest distance- trial 1 - When provided with a graph of an object's velocity as a function of time, the slope of the curve represents the change in velocity per unit of time between two instants in time. This quantity is also known as the average acceleration of the object between the two instants in time. In both trials, the slope of the curves are constant. Therefore, the acceleration of the object in both trials remains constant. The slope of the curve in trial 1 is zero, but the slope of the curve in trial 2 is nonzero. Therefore, the acceleration of the object in trial 2 is greater than the acceleration of the object in trial 1. When provided with a graph of an object's velocity as a function of time, the area bound by the curve and the horizontal axis for a specific time interval represents the change in position of the object during the time interval. This quantity is also known as the displacement of the object between two instants in time. In both trials, the object does not change its direction. Therefore, the displacement of the object is equal to the distance traveled by the object. The area bound by the curve in trial 1 is greater than the area bound by the curve in trial 2. The object travels a greater distance in trial 1 than in trial 2.
A ball is thrown straight up in the air. When the ball reaches its highest point, which of the following is true?
It has zero velocity
Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. Which of the following graphs best represents the vertical displacement of rock X as a function of time starting from immediately after the rock is released from rest? Take the positive direction to be downward.
Line curved upward - The slope of the displacement versus time graph should initially be zero or horizontal to indicate that the initial speed of the rock is zero. This particular graph indicates the correct initial speed of the rock. Since the rock is released from rest, it should fall in the downward (positive) direction, and the slope should increase in the positive direction since the acceleration due to gravity vector is also pointing in the positive direction. This graph displays all of the features that have been previously described.
A toy car has a battery-powered fan attached to it such that the fan creates a constant force that is exerted on the car so that it is propelled in the opposite direction in which the fan blows air. The car has a carriage that allows a student to attach objects of different masses, as shown above. The fan has only one speed setting. All frictional forces are considered to be negligible. Which of the following procedures could be used to determine how the mass of the fan-car-object system affects the acceleration of the system?
Measure the mass of the system using a balance, activate the fan, measure the distance traveled by the system at a known time by using a stopwatch, and repeat the experiment for several trials with different objects added to the carriage. - The mass of the fan-car-object system can be found by using a mass balance. The fan will propel the car forward with a constant force in all trials of the experiment. The meterstick can be used to measure the displacement of the toy car after a stopwatch is used to record a time in which the system travels. The following equation can be used to determine the acceleration of the system: x=x0+vxot+12axt2 (with the initial speed of the system equal to zero). Newton's second law of motion equation could be applied to determine the relationship between the three quantities within the equation: ΣFx=max.
A block of mass M is attached to a modified atwood machine and is accelerated upward at 3a by a constant force Fo. What is the weight of the block
Mg - Weight is a gravitational force exerted on a mass when it is within a gravitational field created by another mass. Weight can be calculated by F=Mg
A person driving a car suddenly applies the brakes. The car takes 4 s to come to rest while traveling 20 m at constant acceleration. Can the speed of the car immediately before the brakes were applied be determined without first determining the car's acceleration.
No, because the acceleration is needed to use standard equations such as change of x= V^ot + 1/2 at^2
A block is placed on an inclined plane and remains stationary, as shown in the figure above. A student claims, "The block remains stationary because as gravity tries to pull the block down the ramp, the block exerts an equal and opposite force on itself up the ramp." Is the student's claim correct? Justify your answer.
No. Newton's third law state the block cannot exert a force on itself - The claim incorrectly asserts that the net force on the block is zero due to the block exerting a force on itself. This is a violation of Newton's third law.
identical spheres are dropped from a height of 100 m above the surfaces of both Planet X and Planet Y. The position of the spheres as a function of time is recorded as the spheres fall. These data are shown in the graphs above. WHich planet exerts a great gravitational force on the sphere, and what evidence supports this conclusion
Planet Y, because the magnitude of the slope of the curve increases at a faster rate - If a planet exerts a greater force due to gravity, the the acceleration due to gravity of an object would be greater Fgravity= mg. This greater acceleration is evidence by the greater rate of change of the slope of the graph for Planet Y
Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. After Rock YY is released from rest several seconds after Rock XX is released from rest, what happens to the separation distance SS between the rocks as they fall but before they reach the ground, and why? Take the positive direction to be downward.
S increases because at all times Rock X falls with a greater speed than Rock Y. - Rock X and Rock Y accelerate downward from the cliff toward Earth at the same rate, which means that both rocks gain their respective downward speeds at the same rate. This means that the numerical difference between their speeds remains the same as they fall toward Earth. However, at all times, Rock X will have a greater downward speed than Rock Y since Rock X has fallen for a greater interval of time. Therefore, between the time Rock Y is released and when it hits the ground, Rock X will have fallen a greater distance than Rock Y. Therefore, the separation distance between the rocks increases as they fall.
An object travels along a straight, horizontal surface with an initial speed of 2 m/s. The position of the object as a function of time is given in the table. Which of the following graphs represents the object's velocity as a function of time?
Straight line starting at 2
An object is at rest on the ground. The object experiences a downward gravitational force from Earth. Which of the following predictions is correct about why the object does not accelerate downward? Select two answers. Justify your selections.
The bonded molecules of the object are repelled upward by the bonded molecules of the ground with the same magnitude as the gravitational force downward on the object. The normal force is exerted upward on the object from the ground with the same magnitude as the gravitational force downward on the object. Explanations: - he object and the ground are considered to be in direct contact. The object and the ground are composed of bonded particles that exist on the atomic level. The interaction of these particles results in an electric force that is exerted on the ground from the object and an electric force that is exerted on the object from the ground. Both electric forces are repulsive, are exerted on different objects, and are opposite in directions. For the object on the ground, an upward electric force is in the opposite direction as the gravitational force and has the same magnitude as the gravitational force on the object. This causes the object to be in static equilibrium. - A normal force can be explained as the electrostatic repulsion force on one object's bonded molecules from another object's bonded molecules as a result of the two objects essentially being in contact with each other. This upward electrostatic repulsion is in the opposite direction as the gravitational force and has the same magnitude as the gravitational force on the object. This causes the object to be in static equilibrium.
A 1500 kg car traveling along a road is hit by a 0.1 kg rock that creates a small crack in the car's windshield. Which of the following describes the interaction between the windshield and the rock?
The car exerts a force on the rock, and the rock exerts a force on the car. The two forces are equal in magnitude - According to Newton's third law, forces between two objects always occur in pairs (action-reaction pairs). The forces are equal in magnitude and opposite in direction.
A small cart is rolling freely on an inclined ramp with a constant acceleration of 0.50 m/s ^2 in the -x direction. At time t=0, the cart has a velocity of 2.0 m/s in the +x direction. If the cart never leaves the ramp, which of the following statements correctly describes the motion of the cart at a time t> 5s?
The cart is traveling in the -x direction and is speeding up
Two students, Student XX and Student YY, stand on a long skateboard that is at rest on a flat, horizontal surface, as shown. In order to get the student-student-skateboard system to accelerate, Student XX claims that Student YY should apply a force on Student XX while both students stand on the skateboard. Which of the following statements is true regarding the claim made by Student XX?
The claim is incorrect because both students are internal to the student-student-skateboard system, and internal forces within a system cannot cause the system to accelerate. - According to Newton's third law of motion, if Student Y exerts a force on Student X, then Student X exerts a force of equal magnitude, but in the opposite direction, on Student Y. Since both students are part of the student-student-skateboard system, these two forces combine to contribute zero net force on the system. An external force or forces must be present for there to be a nonzero net force, which by Newton's second law is necessary for the system to accelerate.
Two objects, X and Y, move toward one another and eventually collide. Object X has a mass of 2M and is moving at a speed of 2Vo to the right before the collision. Object Y has a mass of M and is moving at a speed of Vo to the left before the collision. Which of the following describes the magnitude of the forces F the objects exert on each other when they collide
The force exerted bt X on Y is F to the right, and the force exerted by Y on X is F to the left. - When objects exert forces on each other, the forces are equal in magnitude and opposite in direction
A student pulls a block over a rough surface with a constant force FP that is at an angle θ above the horizontal, as shown above. If FP remains constant but the angle θ is increased, which of the following is true at some later time?
The force of friction between the block and surface will decrease - If the angle is increased, then the normal force acting on the block will decrease (because the force of pull upward increases). The force of friction is related to the normal force by the equation fK=μKFN. Therefore if the normal force decreases, so will the force of friction acting on the block.
Students connect a spring scale to a block on a rough horizontal surface. The students use the spring scale to measure the magnitude of the horizontal force needed to pull the block at a constant speed. Which of the following statements explains why two forces exerted between objects are equal in magnitude?
The frictional forces that the block and the surface exert on each other, because objects always exert forces of equal magnitude on each other. - The block and the surface exert a frictional force on each other, and these forces are a Newton's third-law pair. Claim: The frictional forces that the block and the surface exert on each other are equal in magnitude. Evidence: By Newton's third law, objects always exert forces of equal magnitude on each other.
A satellite orbits Earth. The only force on the satellite is the gravitational force exerted by Earth. How does the satellite's acceleration compare to the gravitational field at the location of the satellite? Select two answers.
The gravitational field and the acceleration point in the same direction. The magnitudes of the acceleration and the gravitational field strength are equal.
A spring-loaded launcher has a mass of 0.60 kg= and is placed on a platform 1.2m above the ground. The force of friction is negligible between the platform and the launcher. The launcher fires a 0.30kg ball that lands a distance D to the right of the platform, as shown in the diagram above. Which of the following explanations is true?
The launcher will fall off the platform and land D/2 to the left of the platform because the launcher is twice the mass of the ball. - The launcher will have half the speed of the ball after the ball is launched. Evidence: Newton's third law indicates that the force on the ball and the force on the launcher will be equal in magnitude. Reasoning Statement: The acceleration of the launcher will be half the acceleration of the ball, so the launcher will travel half the distance the ball travels.
An object is launched upward at angle θ0 above the horizontal with a speed of v0. The trajectory and three positions of the object, X, Y, and Z, are shown in the figure. Position X is higher than position Z with respect to the ground, and position YY is at the object's maximum vertical position. Which of the following claims is correct about the system that consists of only the object?
The object's acceleration is the same at positions X, Y, and Z - At all points along the object's trajectory, the object's acceleration is the acceleration due to gravity that is always directed toward the center of Earth, or, in this case, toward the ground. The object does not accelerate in the horizontal direction at any point along the object's trajectory. Therefore, the object's acceleration remains the same at all points along the object's trajectory.
A student sets up an experiment to determine the inertial mass of a cart. The student has access to the following measurement equipment: a spring scale, a meter stick, and a stopwatch. The student uses the spring scale to pull the cart starting from rest along a horizontal surface such that the reading on the spring scale is always constant. All frictional forces are negligible. In addition to the spring-scale reading, which two of the following quantities could the student measure with the available equipment and then use to determine the inertial mass of the cart? Select two answers.
The total distance traveled by the cart after it has been in motion. The time during which the cart is in motion. Explanations: - The meterstick can be used to measure the total distance traveled by the cart. The distance and time can be used to determine the acceleration of the cart by using the equation x=x0+v0xt+12axt2 where the initial velocity v0x is zero. Once the acceleration of the cart has been determined, it can be used with the spring-scale reading and the equation for Newton's second law of motion a→=ΣF→m to determine the inertial mass of the cart.
A student uses an electronic force sensor to study how much force the student's finger can apply to a specific location. The student uses one finger to apply a force on the sensor, and data collected from two trials are shown in the table. During which trial, if any, does the student's finger experience the greatest electromagnetic force?
Trial 2, because the students finger applied the largest force to the sensor. - rial 2 is the trial in which the student exerted the greatest force on the sensor. Based on Newton's third law of motion, the force that the student applies to the sensor will result in the sensor exerting a force of the same magnitude back onto the student's finger. While the force that the sensor applies to the student's finger is typically classified as a normal force, the normal force arises from the electromagnetic interactions of atoms and molecules at the atomic level that typically experience a repulsive force.
Which of the following experiments could be used to determine the inertial mass of a block?
Use a spring scale to exert a force on the block. Measure the acceleration of the block and applied force - The inertial mass can be determined using Newton's second law: a=F/m
Two identical blocks, block A and block B, are placed on different horizontal surfaces. Block A is initially at rest on a smooth surface, while block B is initially at rest on a rough surface. A constant horizontal force of magnitude Fo is exerted on each block. After the force has been applied for a time change of t, the speeds of blocks A and B are Va and Vb, respectively. Which of the following claims indicates the correct relation between Va and Vb provides the best justification for the relation
Va> Vb. The forces between the atoms in a block and the atoms in a surface opposite the motion of the block and are greater, on average, for block B - The interatomic forces between the atoms in a block and the atoms in a surface oppose the motion of the block, If the horizontal force is exerted on each block, more force is required to move a block over a rough surface due to the microscopic ridges that impede the average movement of the block atoms. Accordingly, the speed of the block atoms moving over the smooth surface will be faster than the speed of the blocka toms moving over the rough surface.
The amusement park ride shown above takes riders straight up a tall tower and then releases an apparatus holding seats. This apparatus free-falls back to Earth and is stopped safely right above the ground. Which of the following indicates the magnitude of the gravitational force exerted on a rider of mass mm on the way up and on the way down?
Way up and way down are equal to mg - The gravitational force on an object near the surface of Earth always has magnitude mg
An object travels along a straight, horizontal surface with an initial speed of 2 m/s. The velocity of the object as a function of time is given in the table above. Which of the following graphs represents the object's acceleration as a function of time?
acceleration with straight line at 2
An object is thrown into the air at an upward angle 0 with respect to the horizontal with a speed of vo. At its maximum height, the speed of the object is
less than vo
Rock XX is released from rest at the top of a cliff that is on Earth. A short time later, Rock YY is released from rest from the same location as Rock XX. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. Which of the following graphs correctly shows the vertical velocity of rock X as a function of time? Take the positive direction to be upward
line below time - The positive direction is considered to be upward. Therefore, rock X should have an acceleration is presented by the negative slope of the curve, because the slope of the curve of a velocity- versus- time graph for an object's motion represents the acceleration of the object. Furthermore, since the rock is released from rest, its initial velocity should be zero
Block A is placed on a rough surface inclined at an angle O above the horizontal. A taut string connects block A over a pulley to block B, which hangs from the string, as shown below. The masses of blocks A and B are Ma and Mb respectively. At time t=0, block A is sliding up the slope as block B falls, and the blocks are both slowing down. Assume that the mass and friction of the pulley are negligible. The two blocks eventually stop and reverse direction. Which of the following graphs best predicts the acceleration of block A as it moves up and down the rough, inclined surface? Assume that the positive direction points down the slope.
the lines are both positive but the first one is on top and the second one is on the bottom -The acceleration of block A is always down the slope, but the direction of the frictional force changes when the block changes direction and begins to oppose the component of gravity down the slope.
A ball is thrown vertically into the air and is caught at the same height from which it was thrown. If air resistance can be ignored, the time it takes traveling upward compared to the time it takes traveling downward is
the same
Two objects, object X and object Y, are held together by a light string and are released from rest near a planet's surface in the orientation that is shown in the figure. Object X has a greater mass than object Y. A graph of the acceleration as a function of time for the system's center of mass is shown for the 4s. The positive direction is considered to be upward. How does the speed of object X vx compare to that of the system's speed vs after the objects have fallen for 4s ?
vx=vs
Toy car W travels across a horizontal surface with an acceleration of aw after starting from rest. Toy car Z travels across the same surface toward car WW with an acceleration of azaz after starting from rest. Car WW is separated from car Z by a distance dd. Which of the following pairs of equations could be used to determine the location on the horizontal surface where the two cars will meet, and why?
x=x0+v0xt+12axt2x=x0+v0xt+12axt2 for car W, and x=x0+v0xt+12axt2x=x0+v0xt+12axt2 for car Z. Since the cars will meet at the same time, solving for tt in one equation and placing the new expression for tt into the other equation will eliminate all unknown variables except x.
