Conservation of Energy (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

Two blocks are connected by a string that passes over a pulley, as shown in Figure 1. Block 1 is on a horizontal surface and is attached to a spring that is at its unstretched length. Frictional forces are negligible in the pulley's axle and between the block and the surface. Block 2 is released from rest and moves downward before momentarily coming to rest.

The spring constant of the spring is , the mass of Block 1 is and the mass of Block 2 is . Block 2 starts from rest and speeds up, then it slows down and momentarily comes to rest at a position below its initial position. is the distance moved by Block 2 before momentarily coming to rest.

Derive an expression for the distance that Block 2 travels before momentarily coming to rest. Express your answer in terms of , , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

Indicate whether the total mechanical energy changes or not as Block 2 moves downward.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ changes ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ does not change

Justify your reasoning.

Starting with the conservation of energy principle, derive an expression for the speed, , of the sphere at the bottom of the vertical circle in terms of the length of the string, .

A projectile is fired from level ground with speed  at an angle  to the ground, where . The projectile is fired from a few centimeters before position , reaches its maximum height at position , and lands on the ground at position

The energy bar charts in Figure 1 represent the gravitational potential energy and the kinetic energy of the projectile as it passes through positions , and . The bar chart at position is complete. Draw shaded rectangles to complete the energy bar charts in Figure 1 for positions and .

• Positive energy values are above the zero-energy line.

• Shaded regions should start at the dashed line representing zero energy.

• Represent any energy that is equal to zero with a distinct line on the zero-energy line.

• The relative height of each shaded region should reflect the magnitude of the respective energy consistent with the scale shown.

Figure 2

Figure 1

In Experiment 1, a block is initially at position and in contact with, but not attached to, an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position to , as shown in Figure 1. The block compresses the spring by an amount . The block is then released. At the block enters a rough part of the track and eventually comes to rest at position . The coefficient of kinetic friction between the block and the rough track is .

On Figure 2, sketch and label graphs of both the kinetic energy, , of the block and the potential energy, , of the block as a function of position between and . You do not need to calculate values for the vertical axis, but the same vertical scale should be used for both quantities.

Figure 2

Figure 1

In Experiment 1, a cylinder of mass is placed at the top of an incline of length and height , as shown in Figure 1. The cylinder rolls without slipping down the incline and continues rolling along a horizontal surface.

Figure 2

In Experiment 2, the cylinder is again placed at the top of the incline. A block of mass is placed at the top of a separate rough incline of length and height , as shown in Figure 2. When the cylinder and the block are released at the same instant, the cylinder begins to roll without slipping while the block begins to accelerate uniformly.

Estimate the comparative translational speeds of the cylinder and block as they reach the bottom of their respective inclines.

Justify your reasoning using ideas about energy conservation.