Question

How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s^–2.

Answer 1

Given: 

Mass of dumb-bell, \( m = 10 \, \text{kg} \)
Height, \( h = 80 \, \text{cm} = 0.8 \, \text{m} \)
Acceleration due to gravity, \( g = 10 \, \text{m s}^{-2} \)

Step 1: Find the velocity just before hitting the floor

Using the formula of motion:
\[ v^2 = u^2 + 2 g h \]
Initial velocity, \( u = 0 \)
\[ v^2 = 0 + 2 \times 10 \times 0.8 = 16 \]
\[ v = \sqrt{16} = 4 \, \text{m/s} \]

Step 2: Calculate momentum transferred to the floor

Momentum, \( p = m v \)
\[ p = 10 \times 4 = 40 \, \text{kg m/s} \]

Answer:

The dumb-bell will transfer a momentum of 40 kg·m/s to the floor.