A ball mass 150g with intial velocity 12 m/s strikes a bat and bounce back with velocity 20m/s .find average force

In answer please tell how you take intial velocity in negative =-12m/s

To find the average force exerted on the ball during the collision with the bat, we can use the impulse-momentum theorem. This theorem states that the change in momentum of an object is equal to the impulse applied to it. Let's break down the problem step by step.

Understanding Momentum and Impulse

Momentum (p) is defined as the product of an object's mass (m) and its velocity (v):

p = m × v

Impulse (J) is the change in momentum, which can also be expressed as the average force (F) multiplied by the time duration (Δt) over which the force acts:

J = F × Δt

Calculating Initial and Final Momentum

First, we need to determine the initial and final momentum of the ball. The mass of the ball is given as 150 grams, which we convert to kilograms for standard SI units:

• Mass (m) = 150 g = 0.150 kg

The initial velocity (u) of the ball is 12 m/s. However, since the ball strikes the bat and bounces back, we consider the direction of the velocities. By convention, we can take the direction towards the bat as negative. Thus, the initial velocity becomes:

• Initial velocity (u) = -12 m/s

The final velocity (v) after bouncing back is 20 m/s in the opposite direction, which we can take as positive:

• Final velocity (v) = 20 m/s

Calculating Change in Momentum

Now, we can calculate the initial and final momentum:

• Initial momentum (p_initial) = m × u = 0.150 kg × (-12 m/s) = -1.8 kg·m/s
• Final momentum (p_final) = m × v = 0.150 kg × 20 m/s = 3.0 kg·m/s

The change in momentum (Δp) is given by:

Δp = p_final - p_initial

• Δp = 3.0 kg·m/s - (-1.8 kg·m/s) = 3.0 kg·m/s + 1.8 kg·m/s = 4.8 kg·m/s

Finding Average Force

Now that we have the change in momentum, we can find the average force. If we assume the time duration of the collision (Δt) is known, we can rearrange the impulse formula:

F = Δp / Δt

For example, if the collision lasts for 0.1 seconds, the average force would be:

• F = 4.8 kg·m/s / 0.1 s = 48 N

In summary, the average force exerted on the ball during the collision can be calculated using the change in momentum divided by the time duration of the collision. Remember, taking the initial velocity as negative is a way to account for the direction of motion, which is crucial in physics problems involving collisions.