Find out the impact-force:
A mass of 3 kg ball freely falls from a height of 2 metres on an anvil, & rise 0.5 metre after the blow. If the duration of impact is (1/50)^{th} of a second, find out the impact-force (i.e. Force because of impact) on the mass. State the total reaction offered by the anvil on the mass.
Solution
H_{1} = Fall of the ball = 2 m
Suppose vertically upward direction as the direction for all the vectors such as momentum forces etc.
V1 = Initial velocity of ball just before impact on the anvil. (Downward direction implies - ve)
H _{2 } = Rising of the ball after impact = 0.5 m
V_{2} = Upward velocity (i.e. + ve) after impact
Mass of the ball (m) = 3 kg.
F × dt = Change in momentum = m (V_{2} - V_{1} )
Impact force on the mass = m (V_{2} - V_{1} ) /(dt )
= 3 (3 √g ) × 50
= 450 √g N.
Impact force on the anvil is downward
= - 450 √g Newtons;
where g = 9.8 m / sec^{2} .
Considering weight of mass W = 3 × 9.8 ≈ (30) N or (3 g ) N the total upward reaction at Anvil = (450 √g + 30) N.