If each ball has the same mass, 0.16 kg, determine the total momentum of the system consisting of the four balls immediately after the collision. (Assume v1 = 0.33 m/s, θ1 = 70°, v2 = 0.49 m/s, θ2 = 30°, v3 = 0.27 m/s, v4 = 0.48 m/s.)
A 4.0-kg object has a forward momentum of 20. kg•m/s. A 60. N•s impulse acts upon it in the direction of motion for 5.0 seconds. A resistive force of 6.0 N then impedes its motion for 8.0 seconds.
The momentum conservation equation can be written as Since the balls are identical, their masses are the same. That is, m A = m B = m. The equation can be rewritten as: Since each term of the equation contains the variable m, we can divide through by m and cancel m's from the equation. The equation can be rewritten as:
So we have one half times 110 plus 0.41 kilograms, times 8.0631 meters per second and that is squared, then subtract from that one half times 110 kilograms times eight meters per second squared, plus one half times 0.41 kilograms times 25 meters per second squared. This gives a change in kinetic energy of negative 59.1 joules.
There are four forces acting upon the object as shown in the free-body diagram at the right. The two vertical forces must balance since there is no vertical acceleration. Since the mass and the acceleration are known, the net force can be computed:
This problem is similar to the two previous problems in many respects: the free-body diagram is identical or similar and the acceleration is not given but determinable from the kinematic information.