Question

A. enter an expression for the magnitude of the impulse delivered to the ball by the ground, in terms of fmax and the time intervals δt1 and Δt2.

b) For the time intervals Δt1 = 2.5 ms and Δt2 = 6.5 ms, what is the magnitude of the maximum force between the ground and the ball, in newtons?

Answer 1

To find the magnitude of the impulse delivered to the ball by the ground, use the formula Impulse = fmax * (δt1 + Δt2). To find the magnitude of the maximum force between the ground and the ball, use the formula Force = impulse / Δt.

Step-by-step explanation:

When a ball bounces off the ground, it experiences an impulse. The magnitude of the impulse delivered to the ball by the ground can be calculated using the formula:

Impulse = change in momentum = F * Δt

Where F is the force applied on the ball by the ground and Δt is the time interval of the collision. In this case, the time intervals are δt1 and Δt2. Therefore, the expression for the magnitude of the impulse delivered to the ball by the ground can be written as:

Impulse = fmax * (δt1 + Δt2)

To find the magnitude of the maximum force between the ground and the ball, we can use the equation:

Force = impulse / Δt

In this case, Δt is the time interval of the collision (0.024s). Substituting the given values, we get:

Force = fmax * (δt1 + Δt2) / Δt

Now you can calculate the magnitude of the maximum force between the ground and the ball by substituting the appropriate values into the equation.

Answer 2

To find the impulse delivered to the ball by the ground, we use impulse's definition involving the change in momentum or the product of average force and contact time. Since we don't have direct information about fmax, we cannot express impulse just in terms of fmax and the time intervals without considering mass and velocity change. An assumed constant maximum force (fmax) during impact would allow the expression Impulse = fmax x Δt.

Step-by-step explanation:

To calculate the magnitude of the impulse delivered to the ball by the ground, we first need to understand that impulse is defined as the change in momentum (ΔP) and can also be calculated by multiplying the average force (Φ) exerted on an object by the time (Δt) the force is applied. Impulse is given by the equation Impulse = Φ × Δt = m × Δv, where m is mass and Δv is the change in velocity. For the ball, we need to calculate the change in velocity when it hits and then leaves the ground. This velocity change can be found using the conservation of energy or kinematic equations for the ball's motion before and after the bounce.

In this case, the expression for the impulse would not be solely in terms of fmax, δt1, and Δt2 because there is not enough information to directly relate fmax to the impulse without considering the ball's mass and velocity change. However, if fmax represents the maximum force during the impact time Δt (where Δt = Δt1 + δt2), we can use Impulse = fmax × Δt as a general expression, assuming fmax is constant during the contact time.