Question

A steel ball is dropped onto a hard floor from a height of a)50 m and rebounds to a height of a)45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 0.0800 ms (8.00×10−5s). (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

Calculate the velocity just before it strikes the floor.
a) v_{{before}} = sqrt{2gh_{{initial}}}
b) v_{{before}} = frac{2gh_{{initial}}}{t_{{floor}}}
c) v_{{before}} = frac{g ⋅ t_{{floor}}}{2h_{{initial}}}
d) v_{{before}} = frac{2h_{{initial}}}{gt_{{floor}}}

Answer 1

The velocity just before the ball strikes the floor is 6.93 m/s, and the velocity just after it leaves the floor on its way back up is 3.92 m/s. The acceleration during contact with the floor is -37,525 m/s^2. The amount of compression during the collision cannot be accurately calculated without knowing the coefficient of restitution.

Step-by-step explanation:

To calculate the velocity just before the ball strikes the floor, we can use the equation v_before = sqrt(2gh_initial), where g is the acceleration due to gravity (9.8 m/s^2), and h_initial is the height from which the ball is dropped (1.50 m). Plugging in the given values, we find that v_before = sqrt(2 * 9.8 * 1.50) = 6.93 m/s.

To calculate the velocity just after the ball leaves the floor on its way back up, we can use the equation v_after = (g * t_floor) / 2, where t_floor is the duration of the contact with the floor (0.0800 ms or 8.00 * 10^-5 s). Plugging in the given values, we get v_after = (9.8 * 8.00 * 10^-5) / 2 = 3.92 m/s.

The acceleration during contact with the floor can be calculated using the equation a = (v_after - v_before) / t_floor. Substituting the values we calculated earlier, we find a = (3.92 - 6.93) / 8.00 * 10^-5 = -37,525 m/s^2 (negative sign indicating deceleration).

To calculate the amount of compression during the collision with the floor, we need to know the coefficient of restitution, which measures the ability of the ball to rebound. Without this information, we cannot calculate the compression accurately.