A billiard ball weighing 270 g moves at a speed of 10 m / s and bounces off after impact with the same speed

| September 8, 2021 | education

A billiard ball weighing 270 g moves at a speed of 10 m / s and bounces off after impact with the same speed in absolute value. The initial and final velocity of the ball is 30 degrees perpendicular to the wall, the duration of the impact is 20 ms. What is the average force acting on the ball from the side of the wall during impact?

m = 270 g = 0.27 kg.

V1 = V2 = 10 m / s.

t = 20 ms = 0.02 s.

∠α = 30 °.

Fср -?

Let’s write Newton’s 2 law in vector form for a billiard ball: m * a = Fav.

a = (V2 – V1) / t – definition of acceleration in vector form.

Let us write down the definition of acceleration a for projections onto an axis perpendicular to the plane of the wall.

a = (V2 * cosα – (- V1 * cosα) / t = 2 * V1 * cosα / t.

The average force of impact of the wall against the ball is expressed by the formula: Fav = m * 2 * V1 * cosα / t.

Fav = 0.27 kg * 2 * 10 m / s * cos30 ° / 0.02 s = 232 N.

Answer: the average impact force is Fav = 232 N.



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