Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 30, 31, 32

Impulse

12

2

1

ppdtFJt

t

dt

pdF

Changes in a particle’s momentum are due to impulse, which depends on the time over which the net force acts.

Impulse

Suppose you throw a ball with a mass of 0.4 kg against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. a) Find the impulse of the net force on the ball during its collision with the wall. b) If the ball is in contact with the wall for 0.010 s, find the average horizontal force that the wall exerts on the ball during the impact.

Polar coordinates

A ball of mass m is swung around a circle at the end of a string of length L. The string will break if the tension in it exceeds a critical value, Tc. What is the largest constant angular velocity the ball can have without breaking the string?

A ball of mass m is swung around a circle at the end of a string of length L. What is the minimum the ball can have and still travel in a circle without string becoming slack?

A plane is flying in an arc at the speed of v0. At the top of arc the passengers experience a sense of weightlessness. What is the radius of the arc?

A 3000 kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

Whirling Beaker of Water

Rotational Motion

€

rN

€

mr g

€

Fy = may

N + mg =mV 2

R

N =mV 2

R− mg

V 2

R> g

Platform rotates with angular acceleration (t)=t. A man starts a distance L from the center and walks in along a straight line painted on the platform towards the center. He decreases his distance from the center as a constant rate, vc. What force does the platform exert on the man, as a function of his distance from the center?

Conical pendulum

A race track designer wants to have the cars able to maintain a speed vmax without skidding on a circular track. If the track is flat with a coefficient of friction what does the radius have to be?

HR

A frictionless track contains a circular section of radius R as shown. What is the minimum height at which a block must be started in order for it to go around the loop without falling off the track?

Kinematics

Have a great day!

Reading: Chapter 12Hw: All Chapters 12, 13 problems and exercises