A smooth sphere of mass 1412 grammes was moving horizontally in a straight line at 13.5 metres per second when it hit a smooth vertical wall and rebounded at nine metres per second. Determine the magnitude of the impulse exerted on the sphere.
The sphere is initially travelling at a speed of 13.5 metres per second. After hitting the smooth vertical wall, it is moving in the opposite direction with a speed of nine metres per seconds. If we consider the initial speed to be in the positive direction, we can say that the final speed is negative nine metres per second in the same direction. The change in velocity on impact is, therefore, equal to 13.5 minus negative nine. This is the same as adding nine. The change in velocity is, therefore, equal to 22.5 metres per second.
We’re told that the mass of the sphere is 1412 grammes. There are 1000 grammes in one kilogramme. We can calculate the mass of the sphere in kilogrammes by dividing 1412 by 1000. This is equal to 1.412 kilogrammes. This question asks us to calculate the magnitude of the impulse. We know that impulse is equal to mass multiplied by change in velocity. We need to multiply 1.412 by 22.5. This is equal to 31.77. The impulse exerted on the sphere is 31.77 kilogramme metres per second.