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AP Physics 1: Algebra-Based 2.8 A Describe the Force Exerted on an Object By an Ideal Spring Questions

Describe the force exerted by an ideal spring and relate its magnitude and direction to displacement from the relaxed or equilibrium position.

Syllabus
Effective Fall 2024
Course
AP Physics 1: Algebra-Based

Exam points

  • calculate ideal-spring force from k and extension measured from the relaxed length
  • draw the restoring-force vector toward equilibrium and scale its length with displacement
  • determine spring constant from the slope of a force-extension graph and test linearity
  • design a repeated-load experiment to measure extension and test ideal-spring behaviour
  • sketch the force-position graph for two springs by adding their restoring forces

AP Physics 1: Algebra-Based 2.8 A Describe the Force Exerted on an Object By an Ideal Spring Questions question 1

[Maximum number: 4]

(12 points, suggested time 25 minutes)
A small block of mass m0m_{0} is attached to the end of a spring of spring constant k0k_{0} that is attached to a rod on a horizontal table. The rod is attached to a motor so that the rod can rotate at various speeds about its axis. When the rod is not rotating, the block is at rest and the spring is at its unstretched length L, as shown. All frictional forces are negligible.

Figure 1

Figure 1

Figure 2

Figure 2

Question (a)

(a)

At time t=t1t=t_{1}, the rod is spinning such that the block moves in a circular path with a constant tangential speed v1v_{1} and the spring is stretched a distance d1d_{1} from the spring's unstretched length, as shown in Figure 1. At time t=t2t=t_{2}, the rod is spinning such that the block moves in a circular path with a constant tangential speed v2v_{2} and the spring is stretched a distance d2d_{2} from the spring's unstretched length, where d2>d1d_{2}>d_{1}, as shown in Figure 2.

[ 3 ]

Question (i)

(i)

On the following dots, which represent the block at the locations shown in Figure 1 and Figure 2, draw the force that is exerted on the block by the spring at times t=t1t=t_{1} and t=t2t=t_{2}. The spring force must be represented by a distinct arrow starting on, and pointing away from, the dot.
Note: Draw the relative lengths of the vectors to reflect the relative magnitudes of the forces exerted by the spring at both times.

Figure for Question (i) — AP Physics 1: Algebra-Based
[ 2 ]

Question (ii)

(ii)

Referencing d1d_{1} and d2d_{2}, describe your reasoning for drawing the arrows the length that you did in part (a)(i).

[ 1 ]

Question (b)

(b)

Consider a scenario where the block travels in a circular path where the spring is stretched a distance d from its unstretched length L.

[ 1 ]

Question (i)

(i)

Determine an expression for the magnitude of the net force Fnet F_{\text {net }} exerted on the block. Express your answer in terms of m0,k0,L,dm_{0}, k_{0}, L, d, and fundamental constants, as appropriate.

[ 1 ]
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