Spring Forces AP Physics 1 FRQ – Exam Style Questions etc.
Spring Forces AP Physics 1 FRQ
Unit: 2. Force and Translational Dynamics
Weightage : 10-15%
Exam Style Practice Questions, Spring Forces AP Physics 1 FRQ
Question: (12 points, suggested time 25 minutes)
A projectile launcher consists of a spring with an attached plate, as shown in Figure 1. When the spring is compressed, the plate can be held in place by a pin at any of three positions A, B, or C. For example, Figure 2 shows a steel sphere placed against the plate, which is held in place by a pin at position C. The sphere is launched upon release of the pin. A student hypothesizes that the spring constant of the spring inside the launcher has the same value for different compression distances.
(a) The student plans to test the hypothesis by launching the sphere using the launcher.
i. State a basic physics principle or law the student could use in designing an experiment to test the hypothesis.
ii. Using the principle or law stated in part (a)(i), determine an expression for the spring constant in terms of quantities that can be obtained from measurements made with equipment usually found in a school physics laboratory.
(b) Design an experimental procedure to test the hypothesis in which the student uses the launcher to launch the sphere. Assume equipment usually found in a school physics laboratory is available.
In the table below, list the quantities and associated symbols that would be measured in your experiment. Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table.
(b) Describe the overall procedure to be used to test the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances, referring to the table. Provide enough detail so that another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup.
(c) Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances.
(d) Another student uses the launcher to consecutively launch several spheres that have the same diameter but different masses, one after another. Each sphere is launched from position A. Consider each sphere’s launch speed, which is the speed of the sphere at the instant it loses contact with the plate. On the axes below, sketch a graph of launch speed as a function of sphere mass.
▶️Answer/Explanation
Conservation of Energy
\(\frac{1}{2}kx^{2} = mgh\)
\(k = \frac{2mgh}{x}\)
(b)
- First, use the ruler to measure the compression distance for the spring at each position (A,B,C) – this will be X. Also, measure the mass of the sphere, this will be m.
- Next, compress the spring to a chosen position, piece the pin, and load the sphere.
- Release the pin, and measure the maximum distance (h) that the ball travelling above its release point.
- Repeat the experiment (starting at step 2) multiple times at each position, and repeat it at each of the three positions.
Before ReleaseAfter Release
(c) First, the experiment should be repeats multiple times at each position to limit experimenter uncertainty. At each distance calculate the spring constant with the expression \(K = \frac{2mgh}{x} (ii),\) with the average height at that position as h, that measures mass of the sphere as M, and the measured very close at each of the positions, then the hypothesis is confirms, otherwise, it is disconfirmed.
(d)
\(\frac{1}{2} kx^{2} = \frac{1}{2}mv^{2}\)
\(kx^{2} = mv^{2}\)
\(v^{2} = \frac{kx^{2}}{m}\)
\(v = \sqrt{\frac{kx^{2}}{m}}\) constant
\(v \alpha \frac{1}{\sqrt{m}}\) v