Question

1. A girl weighing 435 N jumps from a tree, and her center of mass falls a vertical distance of 1.50 m. Find the impulse necessary to bring her to rest.

B) Over what time interval must the deceleration last in order that the average force does not exceed 185 N?
A person of mass 72.5 kg is initially at rest on the edge of a large stationary platform of mass 165 kg, supported by frictionless wheels on a horizontal surface. The person jumps off the platform, traveling a horizontal distance of 1.00 m while falling a vertical distance of 0.500 m to the ground. What is the final speed of the platform?

Answer 1

The student's questions involve calculating impulse, time interval for a given average force, and utilizing conservation of momentum and energy to determine the final speed of a platform after a jump.

Step-by-step explanation:

The first part of the question requires calculating the impulse needed to bring a girl to rest who jumps from a tree. Impulse can be found using the change in momentum, which is equal to the weight of the girl times the distance she falls, assuming she comes to rest immediately upon impact. To solve the second part, we need to find the time interval that would result in an average force of 185 N not to be exceeded during the deceleration. This time can be determined using the impulse-momentum theorem and the known maximum average force.

For the second scenario, we can use the principle of conservation of momentum and conservation of energy to find out the final speed of the platform when a person jumps off it. Since the person is initially at rest with the platform, the total momentum before the jump must be equal to the total momentum after the jump, and the kinetic energy of the person is related to the potential energy lost during the fall.

Remember to keep the student engaged and encourage their understanding by providing guidance on how to set up the equations themselves rather than just presenting the final answers.

Answer 2

The impulse required to stop the girl from falling is 652.5 N·s, and the time interval for the deceleration to not exceed 185 N is approximately 3.53 seconds. The final speed of the platform can be determined by conservation of momentum, considering the mass and velocity of the person jumping off.

Step-by-step explanation:

To solve for the impulse necessary to bring the girl to rest, we use the concept of impulse, which is equal to the change in momentum. Since the girl is falling due to gravity, her initial momentum is zero, and her final momentum is her weight (435 N) times the falling distance (1.50 m). The impulse is therefore 652.5 N·s.

To ensure that the average deceleration force does not exceed 185 N, we can calculate the time interval using the impulse-momentum theorem, Impulse = Average Force × Time Interval. With a total impulse of 652.5 N·s and a maximum average force of 185 N, the time interval is approximately 3.53 seconds.

Moving on to the second problem, we apply the conservation of momentum. Since the system is isolated and there are no external horizontal forces, the momentum of the person jumping off the platform is equal and opposite to the momentum of the platform. Using the mass of the person (72.5 kg) and the calculated velocity (from the horizontal and vertical distances jumped), we can find the final speed of the platform.