Tension (College Board AP® Physics 1: Algebra-Based): Exam Questions

i) Define an ideal string.

ii) Describe the nature of the tension in an ideal string.

Describe a non-ideal string.

Identify whether strings in real life scenarios behave as ideal or non-ideal strings. Justify your reasoning.

A light, inextensible string has a length before and after being placed under tension.

i) Name the type of force responsible for maintaining the structure of the string in both cases.

ii) Compare the repulsive forces between electrons in neighboring atoms when the string is under tension and not under tension.

iii) Explain why an inextensible string does not stretch even when a force is applied.

Figure 1

Two blocks are connected by a light string that passes over a pulley, as shown in Figure 1. The masses of the two blocks are and respectively, where . The pulley has negligible mass and spins with negligible friction about its axle. The blocks are released from rest.

The dots in Figure 2 represent the blocks. The gravitational forces exerted on Block A and Block B are represented by the arrows labelled and respectively.

i) On the dots in Figure 2, draw and label the tension forces that are exerted on the blocks. Each force must be represented by a distinct arrow starting on and pointing away from the appropriate dot. The lengths of the arrows should reflect the relative magnitudes of the forces.

Figure 2

ii) Derive an expression for the acceleration of the system in terms of , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii) Determine an expression for the tension in the string in terms of , , and physical constants as appropriate.

Figure 3

The experiment is repeated with a modification. Block A is on a smooth, horizontal tabletop, and Block B hangs over the side of the tabletop, as shown in Figure 3.

For the same values of and , indicate whether the magnitude of the tension in the string in the modified experiment is greater than, less than, or equal to the magnitude of the tension in the string in the first experiment.

⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽ ‎ ‎ ‎‎ ‎ ‎ ‎ ‎ ‎ ‎ ⎽⎽⎽⎽⎽⎽⎽⎽⎽⎽

Justify your answer.

Figure 1

A sphere of mass is attached to a string of length . The sphere swings in a horizontal circle with constant speed , as shown in Figure 1. The string makes an angle with the vertical.

i) On the dot in Figure 2, which represents the sphere, draw and label the forces (not components) that act on the sphere when the sphere is at the position shown in Figure 1. Each force must be represented by a distinct arrow starting on and pointing away from the appropriate dot. The relative lengths of the vectors should reflect the relative magnitudes of the forces exerted on the sphere for any relative values known.

Figure 2

ii) Determine an expression for the horizontal component of the tension in the string in terms of , , , , and physical constants as appropriate.

iii) Determine an expression for the vertical component of the tension in the string in terms of , , , , and physical constants as appropriate.

iv) Starting with Newton's second law, derive an expression for the speed of the sphere. 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 information.

A student makes the following claim:

"If the sphere is swung fast enough, the string will be perfectly horizontal."

Indicate whether this claim is correct or incorrect, and justify your answer.

Figure 1

Two blocks are connected by a light string which is wound around a frictionless pulley, as shown in Figure 1. Block 1, of mass , is placed on a frictionless ramp that makes an angle with the horizontal and Block 2, of mass , is suspended from the pulley.

A student claims that if the blocks have equal mass , then the system will accelerate up the ramp. Indicate whether this claim is correct or incorrect, and justify your answer using qualitative reasoning beyond referencing equations.

Starting with Newton's second law, derive an expression for the tension in the string in terms of , , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

The blocks are moved to a ramp which is inclined at a steeper angle with the horizontal.

Does the tension in the string increase, decrease, or remain the same? Use the equation derived in part b) to justify your answer.