Calculating the Velocity of a Wrecking Ball Using Impulse and Momentum

In this article, we will explore the physics behind a wrecking ball hitting a wall with a specific force and duration. By applying the principles of impulse and momentum, we can determine the initial velocity of the wrecking ball.

Understanding the Physics

The problem at hand involves a 120 kg wrecking ball that strikes a wall with a force of 475 N for 2.3 seconds. This scenario can be analyzed using the principles of impulse and momentum. Impulse is defined as the product of force and time, and it results in a change in momentum.

Impulse and Momentum Equations

Impulse-momentum theorem states that the change in momentum of an object equals the impulse applied on it. This can be written as:

[ text{Impulse} text{Change in Momentum} ]

Expressed mathematically, this is:

[ Fcdot t mcdot (v_f - v_i) ]

Where:

( F ) is the force applied, ( t ) is the time duration, ( m ) is the mass of the object, ( v_f ) is the final velocity, ( v_i ) is the initial velocity.

Assumptions and Calculation Steps

For this problem, we assume that the wrecking ball comes to a complete stop after hitting the wall. Therefore, the final velocity ( v_f ) is 0. We are given:

( m 120 , text{kg} ) ( F -475 , text{N} ) (negative because the force acts opposite the direction of motion) ( t 2.3 , text{s} )

Given these values, we can find the initial velocity ( v_i ) using the impulse-momentum theorem equation:

[ 0 - mcdot v_i Fcdot t ]

Solving for ( v_i ),

[ v_i frac{-Fcdot t}{m} frac{-(-475 cdot 2.3)}{120} , text{m/s} ]

[ v_i frac{1092.5}{120} , text{m/s} ]

[ v_i approx 9.1 , text{m/s} ]

Conclusion

The initial velocity of the 120 kg wrecking ball, given the conditions of stopping after 2.3 seconds with a force of 475 N, is approximately 9.1 m/s. This solution demonstrates how impulse and momentum can be used to solve real-world physics problems.

Further Reading

For those interested in further understanding the concepts of impulse and momentum, explore related physics problems and questions on topics such as delta v, impulsive force, and momentum conservation.