A small steel sphere of unknown mass is launched horizontally at 8.0 m/s toward a…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum
Problem
A small steel sphere of unknown mass m is launched horizontally at 8.0 m/s toward a stationary cart of mass 1.20 kg on a level, frictionless track. After an instantaneously short, perfectly elastic collision, the sphere rebounds horizontally in the opposite direction at 2.0 m/s while the cart moves forward. A photogate placed 0.50 m down-track from the collision point records that the cart passes through 0.50 s after the collision, and the timing device reports an uncertainty of ±0.02 s in this measurement.
Neglect any external horizontal forces during the collision and subsequent motion.
(a) Derive an algebraic expression for the unknown mass m of the sphere in terms of the given speeds and the cart’s mass M=1.20kg.
(b) Using the photogate data, determine the speed V of the cart immediately after the collision and compute the numerical value of m.
(c) Calculate the percentage uncertainty in the value of m that arises from the timing uncertainty.
(d) Using your numerical results, evaluate whether the assumption of a perfectly elastic collision is reasonable by comparing the system’s total kinetic energy before and after the collision.