AP Physics 1 – 2020 Exam Sample Questions Full Solution
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A small sphere of mass M is suspended by a string of length L. The sphere is made to move in a horizontal circle of radius R at a constant speed, as shown above. The center of the circle is labeled point C, and the string makes angle θ0 with the vertical
Two students are discussing the motion of the sphere and make the following statements.
Student 1: None of the forces exerted on the sphere are in the direction of point C, the center of the circular path. Therefore, I don’t see how there can be a centripetal force exerted on the sphere to make it move in a circle.
Student 2: I see another problem. The tension force exerted by the string is at an angle from the vertical. Therefore, its vertical component must be less than the weight Mg of the sphere. That means the net force on the sphere has a downward vertical component, and the sphere should move downward as well as moving around in a circle.
(a) What is one aspect of Student 1’s reasoning that is incorrect? Explain why.
(b) What is one aspect of Student 2’s reasoning that is incorrect? Explain why.
Student 3 correctly derives two equations to relate the tension force FT to the net force Fnet and the other quantities.
(c) Explain how one of the equations can be used to challenge Student 1’s claim.
(d) Explain how one of the equations can be used to challenge Student 2’s claim.
The students observe that the radius R increases as the speed v of the sphere increases. Together, they derive the equation R = v L/g to calculate the radius of the circle R followed by the sphere if its speed is v.
(e) Regardless of whether this equation is correct or incorrect, does it plausibly model the students’ observation about the relationship between R and v? Why or why not?
(f) This equation does not correctly model the relationship between R and v if v is very fast. Explain why.
Instead of moving in a horizontal circle, the sphere now moves in a vertical plane so that it is a simple pendulum, as shown above. The maximum angle θmax that the string makes from the vertical can be assumed to be small. The graph below shows data for the square of the pendulum period T as a function of string length L.
Explain how the above graph would change under each of the following circumstances. Justify your answers.
(g) The mass of the sphere is increased.
(h) The maximum angle θmax is decreased.
(i) The pendulum is taken to the Moon.
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