Application of Newton’s Second Law

8.01 W03D1

Today’s Reading Assignment: W03D1

Young and Freedman:(Review) 5.1-5.3

Concept Question: TensionA cart is placed on a nearly frictionless surface. A force sensor on the cart is attached via a string to a hanging weight. The cart is initially held. When the cart is released and in motion does the tension in the string

1. increase?

2. stay the same?

3. decrease?

4. cannot determine. Need more information.

Review: Tension in a Rope

The tension in a rope at a distance x from one end of the rope is the magnitude of the action-reaction pair of forces acting at that point ,

left,right right,left( ) ( ) ( )T x x x= =F Fr r

Table Problem: Capstan

A device called a capstan is used aboard ships in order to control a rope that is under great tension. The rope is wrapped around a fixed drum of radius R, usually for several turns (the drawing below shows about three fourths turn as seen from overhead). The load on the rope pulls it with a force TA, and the sailor holds the other end of the rope with a much smaller force TB. The coefficient of static friction between the rope and the drum is μs. The sailor is holding the rope so that it is just about to slip. Draw a free body force diagram for the forces acting on a small piece of the rope of arc length Rdθ at an angle θ as shown in figure.

Worked Example: Capstan In the capstan, show that when the rope is just slipping and the load on the rope pulls it with a force TA, then the sailor holds it with a much smaller force TB given by

where μs is the coefficient of static friction and is the total angle subtended by the rope on the drum.

TB =TAe−μsθBA

θBA

Mini-Experiment: Wrapping Friction

Table Problem: Pulling Blocks Consider two blocks that are resting one on top of the other. The lower block has M2 and is resting on a nearly frictionless surface. The upper block has mass M1 < M2. Suppose the coefficient of static friction between the blocks is μs.

§ What is the maximum force with which the upper block can be pulled horizontally so that the two blocks move together without slipping? Identify all action-reaction pairs of forces in this problem. Odd numbered tables do this part

§ What is the maximum force with which the lower block can be pulled horizontally so that the two blocks move together without slipping? Identify all action-reaction pairs of forces in this problem. Even numbered tables do this part.

Mini-Experiment: Two Block Pull

Experiment 1: Force and Motion

Next Reading Assignment: W03D2

Prepare for Exam 1:Topics:Vectors1 & 2 Dimensional KinematicsForce and Newton’s Second Law

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Monday’s Reading Assignment: W04D1

Young and Freedman: 3.4, 5.4-5.5