Question

A 100 kg mass is blown apart into a 60 kg piece and a 40 kg piece. After the blast, the two masses are moving apart with a relative velocity of 60 m/s. The velocity of the 60 kg mass is:

A 5.0 kg mass is moving in a circular path of radius 3.5 m with a constant tangential velocity of 5.0 m/sec. The centripetal force on the mass is:

A 2000 kg car accelerates up to a velocity of 40 m/s in 5.0 seconds. The brakes are applied and the car is brought to a stop. The work done by the friction in the brakes is:

Answer 1

1.

According to Law of conservation of Momentum, Initial Momentum = Final Momentum

Since the initial velocity is zero, Initial Momentum = 0 = Final momentum.

given,   and   .... Eqn (1)

The smaller mass (m2) moves with more velocity (v2),

    So relative velocity,  

Multiplying throughout by 40   

.... Eqn (2)

Eqn (1) -  Eqn (2) where v2 cancels,

2.

Given, mass, m = 5 kg radius, r = 3.5 m velocity, v = 5 m/s

Centripetal Force is given by,  

3.

Given mass, m = 2000 kg   Initial Velocity, u = 40m/s Time, t = 5 s Final velocity, v = 0 m/s ( Car stopped)

Newtons First Equation of motion,

Newtons First Equation of motion, distance covered by the car when it stops   

Work Done by the brakes = Force X displacement

We just taking the positive values