Chapter 1: Q21E (page 264)

On a frictionless, horizontal air table, puck A (with mass $0.250 k g$ ) is moving toward puck B (with mass $0.350 k g$ ), which is initially at rest. After the collision, puck A has a velocity of $0.120 m / s$ to the left, and puck B has a velocity of $0.650 m/s$ to the right. (a) What was the speed of puck A before the collision? (b) Calculate the change in the total kinetic energy of the system that occurs during the collision.

Short Answer

Expert verified

(a) The speed of puck A before collision is $0.79 m / s$ .

(b) The change in kinetic energy is $0.002 J$

Step by step solution

Step 1:Given in the question:

Mass of puck Ais $m_{A} = 0.250 kg$

Mass of puck Bis $m_{B} = 0.350 kg$

Velocity of puck A is $v_{A} = 0.120 m/s$

Velocity of puck B is $v_{B} = 0.650 m / s$ .

Step 2: Law of conservation of momentum:

When two bodies collide each other then the total momentum before collision is equal to the total momentum after collision.

Step 3:(a) Speed of puck A before collision:

The speed of puck A before collision is calculated as follows:

$P_{A i} + P_{B i} = P_{A f} + P_{B f} m_{A} v_{A i} + 0 = m_{A} v_{A f} + m_{B} v_{B f}$

$\begin{array}{rcl} v_{A i} & = & v_{A f} + \frac{m_{B}}{m_{A}} v_{B f} \\ = & - 0.120 + \frac{0.350}{0.250} \times 0.650 \\ = & 0.79 m / s \end{array}$

Hence,the speed of puck A before collision is $0.79 m / s$

(b) The change in the kinetic energy of the system:

The change in the kinetic energy is calculated as follows:

$\begin{array}{rcl} Δ K & = & K_{f} - K_{i} \\ = & \frac{1}{2} m_{A} v_{A f}^{2} + \frac{1}{2} m_{B} v_{B f}^{2} - \frac{1}{2} m_{A} v_{A i}^{2} \\ = & \frac{1}{2} \times (0.25 \times {(0.12)}^{2} + 0.35 \times {(0.65)}^{2} - 0.25 \times {(0.79)}^{2}) \\ = & 0.002 J \end{array}$

Hence, the change in kinetic energy is $0.002 J$ .

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Short Answer

Step by step solution

Step 1:Given in the question:

Step 2: Law of conservation of momentum:

Step 3:(a) Speed of puck A before collision:

(b) The change in the kinetic energy of the system:

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