A 60.0-kg person bends his knees and then jumps straight up....

A $60.0-\mathrm{kg}$ person bends his knees and then jumps straight up. After his feet leave the floor, his motion is unaffected by air resistance and his center of mass rises by a maximum of $15.0 \mathrm{~cm}$. Model the floor as completely solid and motionless. (a) Does the floor impart impulse to the person? (b) Does the floor do work on the person? (c) With what momentum does the person leave the floor? (d) Does it make sense to say that this momentum came from the floor? Explain. (e) With what kinetic energy does the person leave the floor? (f) Does it make sense to say that this energy came from the floor? Explain.

Key Concepts

Impulse-Momentum Theorem

This concept states that the impulse delivered to an object (the product of force and the time interval over which it is applied) is equal to the change in the object's momentum. It is crucial for understanding how forces applied over time can change the velocity and momentum of an object, regardless of whether the object undergoes displacement during the force application.

Work-Energy Theorem

This theorem explains that the net work done on an object by external forces results in a change in its kinetic energy. The work done by a force depends on both the magnitude of the force and the displacement through which it acts, which helps distinguish situations where forces cause momentum changes without necessarily doing work.

Energy Conversion between Kinetic and Potential Energy

This key concept describes how kinetic energy can be transformed into gravitational potential energy as an object gains height in a gravitational field. In jumping, the initial kinetic energy acquired from the push is gradually converted into gravitational potential energy until the upward motion ceases.

Distinction Between Force, Impulse, and Work

While force is the interaction that can change the state of motion, impulse is a measure of force applied over time that changes momentum, and work is the process of energy transfer when a force causes displacement. This distinction is important for understanding situations where forces may impart momentum (through impulse) without performing work if the point of force application does not move.

Transcript

00:01 Okay, we're looking at question 31.

00:04 This question, a 60 -kilogram person bends his knees and jumps straight up.

00:10 So let's see if we can draw this.

00:13 There he is with his knees all bent, jumping straight up.

00:16 Okay.

00:18 After he leaves the floor, his motion is unaffected by air resistance, and his center of mass rises 15 centimeters.

00:27 Call that distance h.

00:31 H is 15 centimeters.

00:33 Okay.

00:34 We pretend the floor is completely solid and motionless.

00:39 Okay.

00:40 A, does the floor impart impulse to person? yes.

00:50 So remember, impulse is a force times a change in time.

01:03 And the floor is exerting a force on the person, right? so the floor exerts a normal force, and that force occurs over some time, so it imparts an impact.

01:18 Okay, does the floor do work? the answer here is no.

01:25 The work is a force dotted with some displacement, so it does exert a force, but the floor does not displace at all.

01:40 So it doesn't move, so it does not do work.

01:45 What momentum does the person leave the floor with? so momentum be the mass of the person times the velocity that they leave the floor? floor width...

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