Grade upto college level Mechanics

A croquet ball with a mass 0.50 kg is struck by a mallet, receiving the impulse shown in the graph (Fig). What is the ball's velocity just after the force has become zero?

Shane Macguire

11 Years agoGrade upto college level

1 Answer

Deepak Patra

11 Years ago

To determine the velocity of the croquet ball just after the force from the mallet has ceased, we can utilize the concept of impulse-momentum theorem. According to this theorem, the impulse applied to an object is equal to the change in momentum of that object. Let's break this down step by step.

Understanding Impulse

Impulse is defined as the change in momentum resulting from a force applied over a certain time. It can be calculated using the formula:

Impulse = Force × Time

In this scenario, you have a graph that indicates how the force changes over time. The area under the force-time graph represents the total impulse delivered to the croquet ball. To find the impulse, you would calculate this area.

Calculating the Impulse

If the force-time graph is a simple shape, such as a rectangle or triangle, you can easily compute the area.
For a rectangle, use the formula: Area = Width × Height.
For a triangle, use: Area = 0.5 × Base × Height.

Let’s assume the area calculated from the graph gives you an impulse of, say, 2 N·s. This means that the croquet ball has received an impulse of 2 Newton-seconds.

Applying the Impulse-Momentum Theorem

The impulse-momentum theorem states:

Impulse = Change in Momentum = m(v_final - v_initial)

Where:

m is the mass of the ball (0.50 kg),
v_final is the velocity just after the impulse,
v_initial is the initial velocity (which we will assume to be 0 m/s if the ball is at rest before being struck).

Solving for Final Velocity

Plugging in the values into the equation:

2 N·s = 0.50 kg (v_final - 0 m/s)

This simplifies to:

2 N·s = 0.50 kg × v_final

Now, isolate v_final:

v_final = 2 N·s / 0.50 kg = 4 m/s

Final Thoughts

Thus, the velocity of the croquet ball just after the mallet has stopped applying force will be 4 m/s. This example illustrates how impulse directly influences an object's momentum, allowing us to find its velocity after a force is applied. Understanding these relationships is crucial in physics, as they apply to a wide range of scenarios involving motion and forces.