A single cart of mass glides without friction along a straight track and collides…

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A single cart of mass

0.60\,\text{kg}

glides without friction along a straight track and collides sequentially with two identical, stationary carts positioned at different points on the track. A computerized measurement system records the cart’s momentum as a function of time: • For

0\le t<1.00\,\text{s}

, the momentum is constant at

+1.8\,\text{kg}\,\cdot\,\text{m}\!/\!\text{s}

. • At

t=1.00\,\text{s}

the momentum instantaneously changes to

+0.60\,\text{kg}\,\cdot\,\text{m}\!/\!\text{s}

and remains at this value until

t=2.00\,\text{s}

. • At

t=2.00\,\text{s}

the momentum instantaneously changes to

-0.90\,\text{kg}\,\cdot\,\text{m}\!/\!\text{s}

and remains at that value for

t>2.00\,\text{s}

. Assume each collision interval lasts

\Delta t = 0.010\,\text{s}

and that the track is level and frictionless. (a) Determine the impulse experienced by the cart during the first collision (

t=1.00\,\text{s}

) and during the second collision (

t=2.00\,\text{s}

). (b) Calculate the average net force exerted on the cart during each collision interval. (c) Using the magnitudes of the cart’s momentum immediately before and after each collision, decide whether each collision is elastic or inelastic. Justify your classification quantitatively. (d) Discuss whether linear momentum is conserved for (i) the single cart alone and (ii) the entire system of colliding carts during each collision. Support your answer with evidence from the data.

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