Question

An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s^–1 to 8 m s^–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer 1

Given: 

Mass of object, \( m = 100 \, \text{kg} \)
Initial velocity, \( u = 5 \, \text{m/s} \)
Final velocity, \( v = 8 \, \text{m/s} \)
Time, \( t = 6 \, \text{s} \)

Step 1: Initial and final momentum

Momentum, \( p = m v \)
Initial momentum: \( p_i = 100 \times 5 = 500 \, \text{kgm/s} \)
Final momentum: \( p_f = 100 \times 8 = 800 \, \text{kgm/s} \)

Step 2: Magnitude of force

Acceleration, \( a = \frac{v - u}{t} = \frac{8 - 5}{6} = 0.5 \, \text{m/s²} \)
Force, \( F = m a = 100 \times 0.5 = 50 \, \text{N} \)

Answer:

Initial momentum = 500 kg·m/s
Final momentum = 800 kg·m/s
Magnitude of force = 50 N