Question
Please Explain
One truck is heading east at 80 miles per hour. Its mass is 3000 kg. A car (m = 1000kg) is heading north at 40 miles per hour. They collide and stick together. How much energy is lost in the collision? What is the velocity and direction of the car/truck? From the shore of a frozen lake, Eli Manning throws a 2 kg football at a velocity of 20 m/s. A person (m = 30kg) standing on the ice (muk = 0.02) catches the ball. What is their velocity immediately after they catch it? How far do they slide before they come to a stop? One fires a bullet (m=50g) at a block of wood (m=2kg) resting on a frictionless surface. The initial velocity of the bullet is 400m/s. After passing through the block, its velocity is 100m/s. What is the velocity of the block? How much energy is lost? A. A particle of 8 kg with a velocity of 40m/s hits a 40 kg particle that is at. rest. The collision is elastic. What arc the final velocities of the particles? A particle of 8 kg with a velocity of 40m/s al0 degree hits another particle of 25 kg that is moving at a velocity of 70m/s at 90 degree . The collision is elastic. What are the velocities and directions of the particles after the collision?
Explanation / Answer
Final vel in east direction = 80*3000/(3000+1000) = 60 mph
Vel in north direction = 40*1000/4000 = 10 mph
Energy lost = 1/2 * 3000*80^2 + 1/2 * 1000*(40^2) - 1/2 * 4000*(60^2 + 10^2)
= 3*10^6 kg (mi/h)^2
1 mi/hr = 0.44 m/s
So, energy lost = 3*10^6 * 0.44^2
= 599534 J
2) By conservation of momentum, v=2*20/(30+2) = 1.25 m/s
Acceleration due to friction = -uk*g = -0.196 m/s^2
Distance slided = -v^2/2a
= 3.986 m/s
3) momentum lost by bullet = momentum gained by block
0.05*(400-100) = 2*(v-0)
v=7.5 m/s
Energy lost = 1/2 * 0.05*(400^2 - 100^2) - 1/2 * 2*7.5^2
= 18.75 J
4) After an elastic collision,
vel of 8 kg block, v1 = [u1(m1-m2)+2*m2u2]/[m1+m2]
= 40*(8-40)/(40+8)
= -26.67 m/s
vel of 40 kg block, v2 = [u2(m2-m1)+2m1u1] / [m1+m2]
= 2*8*40/48 = 13.33 m/s
5) In the formulae in the above question, use u1=40i, u2 = 70j
m1 = 8 kg, m2 = 25 kg
We get v1 = (-20.61i + 106j) m/s
v2 = (19.39i + 36.06j) m/s