In a laboratory investigation two low-friction carts move along a straight track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

In a laboratory investigation two low-friction carts move along a straight track. Cart 1 has mass

m

while cart 2 has mass

3m

. After identical constant forces act on the carts for equal time intervals, both carts acquire the same magnitude of linear momentum

p

. Ignore any external forces after the pushes end. (a) Derive an algebraic expression for the ratio

K_1/K_2

of the translational kinetic energy

K_1

of cart 1 to the translational kinetic energy

K_2

of cart 2 immediately after the pushes end. Express the ratio only in terms of the masses. (b) Using the masses

m = 2.0\,\text{kg}

and

3m = 6.0\,\text{kg}

with

p = 12\,\text{kg}\!\cdot\!\text{m}\!\cdot\!\text{s}^{-1}

, calculate the individual kinetic energies of the two carts and the numerical value of the ratio found in part (a). (c) The carts now enter a section of track where a uniform friction force of magnitude

4.0\,\text{N}

acts opposite the direction of motion for each cart. Explain which cart will travel the greater distance before coming to rest, citing numeric results when appropriate.

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