AP Physics 1 Unit 6 Progress Check

A block of mass 0.4kg on a horizontal surface is attached to a horizontal spring of negligible mass. 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-spring system then experiences simple harmonic motion as described by the graph. The maximum spring potential energy of the block-spring system is most nearly

0.2 J

What is the spring potential energy stored in the spring-block system at position B?

0.9 J

What is the magnitude of the change in potential energy of the block-spring system when it travels from its lowest vertical position to its highest vertical position?

1/2k0(L1+L2)^2

At which of the following times does the spring exert its maximum force on the block?

2 s

A student attaches a 0.6kg block to a vertical spring so that the block-spring system will oscillate if the block-spring system released from rest at a vertical position that is not the system's equilibrium position. The student measures the velocity of the block as a function of time as the system oscillates, as shown in the graph. The spring constant of the spring is most nearly

2.6

A block on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 30N/m. 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-spring system experiences simple harmonic motion, as shown in the graph. What is the change in spring potential energy of the block-spring system from when the block is released to when the block has its greatest speed?

240 J

In one experiment, the students allow the block to oscillate after stretching the spring a distance A. If the potential energy stored in the spring is U0, then what is the change in kinetic energy of the block after it is released from rest and has traveled a distance of A2 ?

3/4 U

A student is asked to perform experiment 1, but with a spring of an unknown spring constant. The student performs four trials of the experiment with blocks of different mass and collects the data that are shown in the table. How should the student graphically analyze the data in order to determine the spring constant of the spring?

Create a graph with the period of oscillation plotted on the vertical axis and the square root of the mass of the block plotted on the horizontal axis. Use the slope of the best-fit line to determine the spring constant.

A block of mass 0.5kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0.0 m. The block is then pulled to x=0.5 m and released from rest so that the block-spring system oscillates between x=−0.5 m and x=0.5 m, as shown in figure 1. A free-body diagram of the object at a particular location is shown in figure 2. Based on the free-body diagram, at which of the following locations could the block be?

Between positionsx=0.0 m and x=0.5 m

The students must conduct an experiment to determine the magnitude of the force exerted on the block when the block is at a position of A2, where A is the amplitude of oscillation for the block-spring system. For each trial, the students attach blocks of different mass m to the spring, stretch the spring a known distance A, release the system from rest, measure the period of oscillation T, and then measure the maximum velocity v of the system. How should students use a graph to determine the magnitude of the force under consideration?

Determine the magnitude of the slope of the best-fit line of T^2 as a function of m. Multiply the result by A/2.

Student Y is at rest while sitting on a swing. Student X stands behind student Y and provides an initial applied force on student Y. Student Y's position on the swing then oscillates. Which of the following claims is correct about student Y?

If student X applies a greater force on student Y, the total mechanical energy of the student Y-Earth system will increase compared to the original situation.

A student must use an object attached to a string to graphically determine the gravitational field strength near Earth's surface. The student attaches the free end of the string to the ceiling and pulls the object-string system so that the string makes an angle of 5 degrees from the object's vertical hanging position. The student then releases the object from rest and uses a stopwatch to measure the time it takes for the object to make one complete oscillation. Which of the following is the next step that will allow the student to determine the gravitational field strength?

Repeat the experiment by changing the length of the string for multiple trials.

A block on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant k0. The other end of the spring is attached to a wall. When the spring is unstretched, the block is located at x=0m, as shown in Figure 1. The block is then pulled to x=0.3m and released from rest so that the block-spring system oscillates between x=−0.3m and x=0.3m. A student creates the graph shown in Figure 2, which shows the kinetic energy of the block-spring system as a function of the block's position. Which of the following mathematical routines can a student use, if at all, to determine the approximate change in the spring potential energy of the block-spring system when the block is moved from a position of x=0.00m to x=0.02m ?

Subtract the kinetic energy of the block at x=0.02m from the kinetic energy of the block at x=0.00m

A block of mass M on a horizontal surface is attached to a horizontal spring of negligible mass. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the block is pulled to a position beyond the spring's natural length and released from rest, the block experiences simple harmonic motion. A graph of the force exerted on the spring as a function of the block's position is shown. A student collects data such that the force that the spring exerts on the block for every 0.25s is plotted on the graph that is shown. Which two of the following claims is correct about the block-spring system during the time in which data were collected? Select two answers.

The block has its maximum acceleration at all times 0.5n, where n is a zero or a whole number. B The block has maximum spring potential energy at all times 0.5n, where n is a zero or a whole number.

A 4.0 kg cube is placed in a container of water. A student observes that the cube floats. The net force exerted on the cube F represents the sum of the force due to gravity and the force exerted on the cube by the water. A force probe is used to measure F as a function of the cube's distance y from the bottom of the container. The graph shows F as a function of y, where the positive direction is upward. Which of the following statements is correct about the motion of the cube if it is released from rest at a vertical position of y=0.05 m?

The cube will oscillate between y=0.05 m and y=0.09 m.

A block of mass M hangs at rest at the bottom of a stationary spring that stretches a distance A from the spring's unstretched length. The block is then pulled down an additional distance A so the spring is stretched a distance 2A , as shown in the figure. The block is released from rest, and the center of mass of the block vertically oscillates a displacement of 2A from its lowest position to its highest position. The lowest vertical position of the block's center of mass is the location at which the gravitational potential energy of the block-spring-Earth system is zero. Which two of the following claims are correct about the mechanical energy of the system? Select two answers.

The kinetic energy of the block is at its maximum when the spring is stretched a distance A from its unstretched length. The potential energy of the system is at its maximum when spring is stretched a distance 2A from its unstretched length.

Student X attaches an object of mass M to the end of a string of length L so that a pendulum is constructed. Student Y attaches an object of mass M to a string of length 4L to construct a second pendulum. Which of the following claims correctly compares the period of Student X's pendulum with the period of Student Y's pendulum?

The period of Student X's pendulum is half the period of Student Y's pendulum.

The gravitational field strength near Jupiter's surface is nearly 2.53 times greater than the gravitational field strength near Earth's surface. Which of the following claims is correct about the period of a pendulum if it oscillates near Jupiter's surface and near Earth's surface?

The period of the pendulum will be greater on Earth.

The students conduct experiment 2 in which the same block is connected to the same spring on a horizontal surface. The spring is stretched a distance L2 beyond its natural length and released from rest, allowing the block-spring system to oscillate. Frictional forces are considered to be negligible. Which of the following claims is correct about how the period of oscillation for the block-spring system in experiment 2 compares with the period of oscillation for the system in experiment 1, and what evidence supports the claim?

The periods of oscillation for experiment 2 and experiment 1 are the same, because the block and the spring used in both experiments are identical.

A student attaches a block to a vertical spring so that the block-spring system will oscillate in simple harmonic motion if the system is released from rest at a vertical position that is not the system's equilibrium position. Which of the following explanations is correct about why the system oscillates in simple harmonic motion about the block-spring system's equilibrium position?

The system oscillates in simple harmonic motion because the block's acceleration is directly proportional to and opposite in direction to the block's displacement from the system's equilibrium position.

A block on a horizontal surface is attached to a horizontal spring of spring constant 50N/m. The other end of the spring is attached to a wall. The block is initially at the equilibrium position of the block-spring system, as shown in the figure. The block is then moved to a position of x=60cm and released from rest so that the system oscillates. A student predicts the kinetic energy of the block-spring system as a function of the block's horizontal position as shown in Graph 1. When an experiment is conducted, the block does not make a complete oscillation because frictional forces were not considered in the student's prediction. Data is collected about the actual kinetic energy of the block-spring system as a function of the block's horizontal position and is used to create Graph 2.

Use Graph 2 to determine the spring potential energy stored in the system at the instant the block is no longer in motion. Subtract this value from the maximum predicted kinetic energy of the block that can be determined from Graph 1.

A student attaches a block to a vertical spring so that the block-spring system will oscillate if the block-spring system is released from rest at a vertical position that is not the system's equilibrium position. Which of the following measuring tools, when used together, can be used to determine the spring constant of the spring? Select two answers.

stopwatch, protractor