A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.

Short Answer

Expert verified

The cylinder is rolling, reaching a maximum height, and then returning to rest.

Step by step solution

01

Position versus Time

The position vs. time sketch is given below,

The body gains height from t = 0 to t = t s. At t, it reaches its maximum height.

The cylinder is attracted back to the earth due to gravitational force; hence it falls back and comes back to the same position from time t s to 2t s.

02

Velocity versus time graph

Initially, the velocity of the cylinder decreases as it climbs up, so there is a pull of gravitational force. When it reaches time t, the velocity becomes zero.

After which, it suddenly falls.

This falling is due to gravitational acceleration.

Figure: Velocity versus time graph

Similarly, to draw acceleration versus time graph.

When a cylinder rolls up an inclined surface, it suffers a negative acceleration.

The acceleration will be positive with a magnitude as it rolls down the hill.

The graph of acceleration vs. time is shown below.

Figure: Acceleration versus time graph

Hence, this graph mentions the motion of a cylinder rolling up and coming back.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the speed of the bird in Exercise 2.4.

Freight trains can produce only relatively small accelerations and decelerations.

(a) What is the final velocity of a freight train that accelerates at a rate of\({\bf{0}}.{\bf{0500}}{\rm{ }}{\bf{m}}/{{\bf{s}}^{\bf{2}}}\)for\({\bf{8}}.{\bf{00}}{\rm{ }}{\bf{min}}\), starting with an initial velocity of\({\bf{4}}.{\bf{00}}{\rm{ }}{\bf{m}}/{\bf{s}}\)?

(b) If the train can slow down at a rate of\({\bf{0}}.{\bf{0500}}{\rm{ }}{\bf{m}}/{{\bf{s}}^{\bf{2}}}\), how long will it take to come to a stop from this velocity?

(c) How far will it travel in each case?

A graph of v(t) is shown for a world-class track sprinter in a\({\bf{100}} - {\bf{m}}\)race. (See Figure 2.67). (a) What is his average velocity for the first 4 s? (b) What is his instantaneous velocity at\(t = {\rm{ }}{\bf{5}}{\rm{ }}{\bf{s}}\)? (c) What is his average acceleration between 0 and 4 s? (d) What is his time for the race?

A swan on a lake gets airborne by flapping its wings and running on top of the water.

(a) If the swan must reach a velocity of6.00 m/s to take off and it accelerates from rest at an average rate of 0.350 m/s2, how far will it travel before becoming airborne?

(b) How long does this take?

A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victime with an initial velocity of and observes that it takes to reach the water.

(a) List the known in this problem.

(b) How high above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free