Question

A 4kg ball having velocity (7i+6j) m/s collides and bounces off a wall with a velocity of (-3i+6j) m/s. The ball is in contact with the wall for 0.01 s.In unit-vector notation, what are a) the impulse and b)the average force on the ball from the wall

Answer 1

Question

A 4 kg ball having velocity (7i + 6j) m/s collides and bounces off a wall with a velocity of (-3i + 6j) m/s. The ball is in contact with the wall for 0.01 s. In unit-vector notation, what are a) the impulse and b) the average force on the ball from the wall.

Answer

$$m = 4 \, kg; \, \overrightarrow{v_1} = 7 \hat{i} + 6 \hat{j} \, \frac{m}{s}; \, \overrightarrow{v_2} = -3 \hat{i} + 6 \hat{j} \, \frac{m}{s}; \, \Delta t = 0.01 \, s$$

a) For the impulse we obtain

$$\tilde{I} = \overrightarrow{\Delta p} = \overrightarrow{p_2} - \overrightarrow{p_1} = m(\overrightarrow{v_2} - \overrightarrow{v_1}) = 4((-3 - 7) \hat{i} + (6 - 6) \hat{j}) \frac{kg * m}{s} = -40 * \hat{i} \frac{kg * m}{s}$$

b)

$$\tilde{F} \Delta t = \tilde{I} \rightarrow \overrightarrow{F} = \frac{\tilde{I}}{\Delta t} = -4000 * \hat{i} \, N$$

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