Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 16, 17, 18

F Find F necessary to drag the box 1 at constant speed. 1 2 Friction everywhere.

The advantage of a pulley What minimum force F is needed to lift the piano of mass M?

WORK (Chapter 7)

2 or 3 D motion Definition of work: Kinetic energy: Work-energy theorem:

A person carries a bag of groceries of mass M with a constant velocity at the same height from the ground. Find the work done by a person on a bag.

Problem 1 p. 122 A man pushes up on a 100 kg block with a force such that it drops from 2 meters to the ground at a constant velocity. a)How much work is done by gravity? b)What is the magnitude of the force he exerts?

A block of mass m starts at the top of an inclined plane. The coefficient of friction between the plane and the block is . Assuming the block slides down the plane calculate the work done by each force.

Work Energy Theorem

A person is pulling a crate of mass M along the floor with a constant force F over a distance d. The coefficient of friction is . (a)Find the work done by the force F on the crate. (b)Same if F changes as F 0 (1+x 2 /d 2 ). (c)Find the work done by the force of friction on the crate (F is constant). (d)Find the net work done on the crate if the crate is pulled with a constant velocity. (e)Find the final velocity of the crate if the crate is pulled with a non-zero acceleration starting from the rest. M

x

Problem 2 p.122 A 3 slug mass is attached to a spring which is pulled out one foot. The spring constant k is 100 pounds/ft. How fast will the mass be moving when the spring is returned to its unstretched length? (Assume no friction.)

A 5.00 kg block is moving at v 0 =6.00 m/s along a frictionless, horizontal surface toward a spring with constant k=500 N/m that is attached to a wall. a)Find the maximum distance the spring will be compressed. b)If the spring is to compress by no more than m, what should be the maximum value of v 0 ?

Quiz Ch7 y A block of mass m slides down on the larger block of mass M (see the figure below). There is non-zero coefficient of friction between the two blocks. Neglect the friction between the block of mass M and the table. 1) Plot the free body diagram for each of the blocks; 2) Find the work done by gravity on the block of mass m (the smaller one) in two coordinate systems shown above, if the height of the inclined plane is H. x x y

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Have a great day! Reading: Chapter 7 Hw: Chapter 7 problems and exercises