Impulse Calculation in a Collision Scenario

When it comes to calculating impulse in a collision scenario, it is essential to consider the principles of momentum transfer and the changes in velocity that occur during the interaction between objects.

In this specific case, a student on a go-cart with a combined mass of 82 kg is moving at 6.2 m/s and collides with a 17 kg cart initially at rest. The collision results in the transfer of momentum from the first cart to the second cart, with the velocity of the student and cart being 5.22 m/s after the collision.

The duration of the collision is 0.20 s, and we are tasked with determining the absolute value of the impulse delivered to the student and the first cart during this interaction.

To calculate the impulse, we can use the equation:

Impulse = Change in Momentum = Mass x Change in Velocity

For this scenario, the mass of the student and the cart is 82 kg, and the change in velocity is 5.22 m/s - 6.2 m/s = -0.98 m/s (negative due to the opposite direction of velocity post-collision).

Therefore, the impulse delivered to the student and the first cart during the collision is:

Impulse = 82 kg x (-0.98 m/s) = -80.36 kg m/s

The absolute value of the impulse is 80.36 kg m/s, which is closest to option b) 97.66 kg m/s.

Understanding how impulse is calculated in a collision scenario is crucial for analyzing the effects of interactions between objects and determining the resulting changes in momentum. To delve deeper into the concepts of impulse and momentum, you can explore additional resources and examples.