Question

A 170 g ball is dropped from a height of 1.8 m , bounces on a hard floor, and rebounds to a height of 1.5 m . The figure(Figure 1) shows the impulse received from the floor. What maximum force does the floor exert on the ball?

Answer 1

When a ball bounces off a hard floor, it experiences a change in momentum due to the impulse received from the floor. The maximum force exerted on the ball by the floor can be calculated by dividing the impulse by the duration of contact. However, the contact time is not given in the question, so we cannot calculate the exact value of the maximum force.

Step-by-step explanation:

When a ball bounces off a hard floor, it experiences a change in momentum due to the impulse received from the floor. The impulse is equal to the change in momentum of the ball and is given by the equation:

Impulse = mass x change in velocity

The maximum force exerted on the ball by the floor can be calculated by dividing the impulse by the duration of contact between the ball and the floor. This force is equal in magnitude and opposite in direction to the force exerted by the ball on the floor.

Let's calculate the maximum force exerted on the ball by the floor using the given information:

Mass of the ball (m) = 170 g = 0.17 kg

Height from which the ball is dropped (h) = 1.8 m

Height to which the ball rebounds (h') = 1.5 m

First, we need to calculate the change in velocity of the ball during the bounce. Using the equation of motion:

Change in velocity = sqrt(2 x acceleration x height)

Where acceleration due to gravity (g) = 9.8 m/s^2, height (h) = 1.8 m, and height (h') = 1.5 m.

Substituting the values:

Change in velocity = sqrt(2 x 9.8 x (1.8 - 1.5))

Change in velocity = sqrt(2 x 9.8 x 0.3)

Change in velocity = sqrt(5.88)

Change in velocity = 2.42 m/s

Next, we can calculate the impulse received by the ball using the equation:

Impulse = mass x change in velocity

Impulse = 0.17 x 2.42

Impulse = 0.4124 kg*m/s

Finally, we can calculate the maximum force exerted on the ball by the floor using the equation:

Force = Impulse / contact time

Let's assume the contact time is t seconds.

Force = 0.4124 / t

Since the contact time is not given, we cannot calculate the exact value of the maximum force exerted on the ball by the floor.

Answer 2

To find the maximum force exerted by the floor on the ball, we can use the concept of impulse. Using the equation for impulse and substituting the given values, we can calculate the force exerted by the floor on the ball to be approximately 341 N.

Step-by-step explanation:

To find the maximum force exerted by the floor on the ball, we need to use the concept of impulse. Impulse is the change in momentum of an object and is given by the product of force and time. In this case, the impulse received by the ball is equal to its change in momentum. Using the equation for impulse, we can calculate the force exerted by the floor on the ball.

The impulse is given by the formula: impulse = force x time. We can rearrange the equation to solve for the force: force = impulse / time. Plugging in the values given in the question, we get the force exerted by the floor on the ball to be:

force = (2 x mass x change in velocity) / time. The mass of the ball is 170 g, which is equal to 0.17 kg. The change in velocity is the difference in the velocity before and after the collision, which can be calculated using the heights. The velocity before the collision is given by the equation: velocity = square root of (2 x acceleration x height) and the velocity after the collision is given by the equation: velocity = square root of (2 x acceleration x rebound height).

Substituting the values, we can calculate the force exerted by the floor on the ball.

force = (0.17 kg x (square root of (2 x 9.8 m/s^2 x 1.8 m) - square root of (2 x 9.8 m/s^2 x 1.5 m))) / 0.024 s.

Calculating the values, the maximum force exerted by the floor on the ball is approximately 341 N.