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Linear Impulse and Momentum (Impact)

Example: The figure below shows the top view of a bowling ball, B, striking the head pin, P,

at an angle θ. The initial speed of the bowling ball is, v_o. The mass of the bowling ball is

M and the mass of the head pin is m. The coefficient of restitution is e. The following

data applies: M = 0.5 slugs, m = 0.025 slugs, v_o = 5 fps, θ = 30^o, e = 0.7. Find the velocity

of the bowling ball and the head pin immediately after impact.

Impact is a special case of linear momentum where the duration of the impulse is small.

Recall the principle of Linear Impulse and Momentum as follows:

t₂

∫ Σ F dt = m v_c2 - m v_c1

t₁

Strategy:

Step 1: Draw free body diagrams showing the impulse acting on the bowling ball and on

the headpin.

Step 2: Calculate the linear impulse acting on the bowling ball and on the head pin.

Then set them equal to the change in linear momentum of the bowling ball

and of the headpin.

Step 3: Apply the definition of coefficient of restitution to relate normal velocities before

and after impact.