Practicing Success
A spherical ball of mass 10-6 kg hits a wall 1000 times per second normally with a velocity of 1000 m/s and rebounds with same velocity along the initial direction. The force experienced by the wall is : |
1 N 3 N 2 N 5 N |
2 N |
Force experienced by the wall can be described as the change in net momentum (transferred to wall) divided by the total time taken. \(\Delta P_{ball} = m \Delta v\) \(\Rightarrow \Delta P_{ball} = 10^{-6}(-1000-1000)\) \(\Rightarrow \Delta P_{ball} = 10^{-6} (-2000)\) \(\Rightarrow \Delta P_{ball} = -2\times 10^{-3} \text{ kg m/s}\) Momentum change transferred to wall : \(\Rightarrow \Delta P_{ball} = -\Delta P_{wall} = 2 \times10^{-3} \text{ kg m/s}\) Net Momentum transferred to wall : \(\Rightarrow P_{net} = 2\times 10^{-3} \times (\text{ no. of times hitting})\) \(\Rightarrow P_{net} = 2\times 10^{-3} \times 10^{3}\) \(\Rightarrow P_{net} = 2 \text{ kg m/s}\) So, force experienced by wall: \(\Rightarrow F = \frac{\Delta P_{net}}{dt}\) \(\Rightarrow F = \frac{2}{1}\) \(\Rightarrow F = 2 \text{ N}\) |