During a laboratory investigation

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

Problem

During a laboratory investigation, cart

A

of known mass

m_A=0.30\,\text{kg}

rolls along a frictionless track and collides head‐on with cart

B

of unknown mass

m_B

. A motion sensor records the velocity of cart

A

before and after the collision: • Just before impact:

v_{Ai}=+1.5\,\text{m}\!/\!\text{s}

• Just after impact:

v_{Af}=+0.40\,\text{m}\!/\!\text{s}

Cart

B

is initially at rest, and the two carts latch together by means of velcro following the collision. The collision duration is

\Delta t = 0.020\,\text{s}

, during which the net external force on the two‐cart system is negligible. Respond thoroughly to each part. (a) Sketch a qualitative graph of the momentum of cart

A

versus time that includes the interval before, during, and after the collision. Clearly label numerical values on the vertical axis and indicate the collision interval. (b) Calculate the impulse delivered to cart

A

during the collision. (c) Determine the mass

m_B

of cart

B

. (d) Compute the ratio of the final kinetic energy of the two‐cart system to its initial kinetic energy. Based on this ratio, classify the collision as elastic or inelastic and justify your answer. (e) Identify one plausible experimental source of error that could cause the calculated value of

m_B

to differ from its actual value and explain the effect of that error on the result.

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