1.A truck with a mass 5000 kg is heading East at 20 m/s. Meanwhile a car with a mass 2500 kg is heading North at 30 m/s. The two vehicles collide at an intersection, get stuck together, and the wreckage keeps moving to some direction.find the speed of the wreckage and the direction it moves to, just after the collision.

Question

2.A horizontal disk (M = 150 g, R = 20 cm, I = MR*2/2 )rotates at 10 rev/min about its axis.(no friction, no torque from outside). An overweight flying bug (m = 15 g) lands vertically on the disk at a point half way to the center. Use the conservation of angular momentum to find the angular speed of the plate just after this collision.

Answer 1

1. Use the fact that the total momentum of truck and car are the same before and after the collision. You will need to consider momenta in both East direction (x axis) and North direction (y axis). We will be happy to critique your work.

2. Use the fact that the toal angular momentum about the disc axis, before and after the bug lands, will be the same.

I w1 = I w2 + m (R/2)^2 w2

(w2/w1) = I/[I + m R^2/4]
= 1/[1 + (m/I) R^2/4]
= 1/[1 + (m/M)(R^2/4)/(R^2/2)]
= 1/[1 + (1/2)(m/M)]

w is the angular speed. w2/w1 is the ratio by which it decreases.

Answer 2

1. Truck moving along east along X direction and car moving north along the Y direction.
Total momentum along the X direction:
5000 * 20 + 0 = 7500 V1 cosine ө
1000 = 75 V1 cosine ө --------------------- (1)
Total momentum along the Y direction:
2500 * 30 + 0 = 7500 V1 sin ө
750 =75 V1sin ө------------------------- (2)
Dividing (2) and (1),
Tan ө=0.75
Ө =370
From equation (2),
V1 sin ө = 10
V1 sin 370 = 10
V1 = 10/sin 370
V1 = 10/0.6
V1 = 16.6 m/s is the velocity of the combined vehicles