Question

1. A 0.4 kg ball hits the ground (vertically) at a speed of 6 m/s, bouncing back in the opposite direction at 4 m/s. Calculate the magnitude of the impulse provided by the ground to the ball.

A. 2 Ns

B. 10 Ns

C. 4 Ns

D. 0.8 Ns

2.Calculate the recoil speed of a 1.4 kg rifle shooting 0.006 kg bullets with muzzle speed of 800 m/s

A. 3.43 m/s

B. 571 m/s

C. 1.22 m/s

D. 6.42 m/s

3. A 20 kg cart moving at 10 m/s bumps from behind an 80 kg cart initially moving at 2 m/s in the same direction. The two carts stick to each other after the collision. Calculate the speed of the carts after they collide.

A. 8.4 m/s

B. 3.6 m/s

C. 7.6 m/s

D. 0.4 m/s

4. A 40 kg cart moving from South toward North at 6 m/s has a totally inelastic collision with a 20 kg cart moving at 3 m/s in the opposite direction. What is the speed and the direction of motion of the two carts just after the collision?

A. 3 m/s toward North

B.5 m/s toward South

C.5 m/s toward North

D.3 m/s toward South

Answer 1

1.

Impulse is given by,

I = dP = change in momentum

I = Pf - Pi = m*vf - m*vi

given, vf = final speed = 4 m/s

vi = initial speed = 6 m/s

m = mass = 0.4 kg

So, I = 0.4*(4 - 6) = -0.8 Ns

Magnitude of impulse = |I| = 0.8 Ns

Therefore correct option is D.

2.

From momentum conservation:

Pf = Pi

m1*v1f + m2*v2f = Pi

given, Pi = 0

m1 = mass of rifle = 1.4 kg

m2 = mass of bullet = 0.006 kg

v1f = final speed of rifle = ??

v2f = final speed of bullet = 800 m/s

So, v1f = -0.006*800/1.4 = -3.43 m/s

then, recoil speed = 3.43 m/s

Therefore correct option is A.

3.

Using momentum conservation before and after collision:

Pi = Pf

m1u1 + m2u2 = (m1 + m2)V

m1 = mass of cart 1 = 20 kg

m2 = mass of cart 2 = 80 kg

u1 = initial speed of m1 = 10 m/sec

u2 = initial speed of m2 = 2 m/sec

V = final speed of both carts after collision = ?

So,

V = (20*10 + 80*2)/(20 + 80) = 3.6 m/s

Correct option is B.

4.

Using momentum conservation before and after collision:

Pi = Pf

m1u1 + m2u2 = (m1 + m2)V

m1 = mass of cart 1 = 40 kg

m2 = mass of cart 2 = 20 kg

u1 = initial speed of m1 = +6 m/sec

u2 = initial speed of m2 = -3 m/sec

V = final speed of both carts after collision = ?

So,

V = (40*6 + 20*(-3))/(40 + 20) = 3.0 m/s (Since +ve value so towards north)

Correct option is A.

Let me know if you've any query.