A cart rests on a frictionless horizontal track

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

10\,\text{kg}

cart rests on a frictionless horizontal track. Beginning at

t=0

, a stream of identical clay blobs, each of mass

0.20\,\text{kg}

, is fired horizontally so that the blobs strike the back of the cart at

4.0\,\text{m}\!/\!\text{s}

relative to Earth. Exactly

5

blobs strike and stick each second for as long as the stream is on. Immediately after contact, each blob comes to rest relative to the cart. Neglect all external horizontal forces. (a) Derive an algebraic expression for the cart’s speed

v(t)

as a function of time

t

(in seconds) while the stream is continuous. Express

v(t)

solely in terms of

t

and numerical constants provided. (b) Using your expression, determine the cart’s speed after

10\,\text{s}

of continuous bombardment. (c) Calculate the cart’s horizontal displacement from its initial position during the

10\,\text{s}

interval. Show all steps clearly.

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