Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 13, 14, 15

H Coefficient of friction:  1) Find the force of friction if the block is at rest. 2) What is the velocity of the block when it reaches the bottom?

Newton’s 3 rd Law For every action there is an equal, but opposite, reaction

Skater Skater pushes on a wall The wall pushes back –Equal and opposite force The push from the wall is a force –Force provides an acceleration –She flies off with some non-zero speed

P m1m1 m2m2 No friction m1m1 Free body diagram m1m1 m1gm1g P N1N1 F 21 m2gm2g F 12 N2N2 m2m2 F 12 =F 21

Quiz a) A crate of mass m is on the flat bed of a pick up truck. The coefficient of friction between the crate and the truck is . The truck is traveling at the constant velocity of magnitude V 1. Draw the free body diagram for the crate. b) The truck starts to accelerate with an acceleration a c. Draw the free body diagram for the crate, if the crate does not slip.

A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?

A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=30 0, what is the minimum magnitude of P to hold the block still? θ P

V0V0 A block of mass m is given an initial velocity V 0 up an inclined plane with angle of incline θ. Find acceleration of the block if a)  = 0 b) non-zero 

A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop?

A Problem With First Year Physics Strings and Pulleys m1m1 m 1, m 2 are given m 2 >m 1 m2m2 String is massless and unstretchable Find accelerations of m 1 and m 2 (assume no friction in pulley)

Block 1, of mass m 1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m 2. The pulley is massless and frictionless and just changes the direction of the tension in the string. The coefficient of friction between the plane and m 1 is the constant . 2 1 Determine what range of values for mass m 2 will keep the system at rest. Find acceleration if mass 2 goes down.

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?

The Elevator Problem

Have a great day! Reading: Chapter 7 Hw: Chapter 6 problems and exercises