4.3. Tension and Pulleys

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1 4.3. Tension and Pulleys

2 Demonstration 1. Calibrate 2 spring scales, put them together horizontally, and pull apart. Do they always show the same force? What are they measuring? 2. Put 2 spring scales together vertically, and calibrate both to zero. If a weight is added at the bottom, will both scales show that weight, or half that weight? Why?

3 Strings and Tension When you pull on a string or rope, it becomes taut. We say that there is tension in the string. Tension is a force. How does its magnitude and direction vary along the string?

4 Strings and Tension If the string were cut in any place, equal and opposite forces would be needed to hold the string together again. All along an uncut string are equal and opposite forces, for no net acceleration.

5 Demonstration Have two people hold a string under high tension. Have a third person cut the string in half. What happens? Why?

6 Strings and Tension In a sense, the string transmits forces from one end to the other. Tie a string to a chair, and pull. The force of the chair s resistance is transmitted to your hand, and you hand s force to the chair.

7 Strings and Tension The tension in a real rope will vary along its length due to the weight of the rope itself. Here, we will assume that all ropes, strings, wires, etc. are massless unless otherwise stated.

8 Strings and Tension Consider a heavy box suspended on a rope attached to a crane. Does the tension on the rope increase or decrease if: (a) the crane accelerates upward? (b) the crane accelerates downward? (c) the crane moves upward with constant velocity? What about a fishing pole?

9 Pulleys: Demonstration 1. How might a pulley change tension? 2. What would the free-body diagram of the balance of forces be for a rope and a pulley: a. For the rope turned 90 degrees? b. For the rope turned 180 degrees? 3. Experiment!

10 Strings, Tension and Pulleys An ideal pulley is one that simply changes the direction of the tension. A man is holding a box at a constant height off the ground by means of a pulley. What are the forces on the box, the rope, the pulley, and the man?

11 Translational Equilibrium Objects with zero acceleration are said to be in equilibrium. For this to happen, the net force on it must be zero: This allows the calculation of unknown forces. Note that the velocity does not need to be zero; just zero acceleration. Translational refers to motion through space.

12 Translational Equilibrium A man is pulling up a bucket at constant velocity. What are the forces acting on the various parts of the system?

13 Translational Equilibrium What are the forces if the man ties the free end of the rope also to the bucket?

14 Translational Equilibrium What are the forces if the man ties the free end of the rope also to the bucket?

15 Example A 1.84-kg bag of clothespins hangs in the middle of a clothesline, causing it to sag by an angle of 3.50 degrees. Find the tension in the line.

16 Demonstration Have two people hold a string under tension. Place a weight in the middle. How much force must they apply to straighten out the string? In a cause-and-effect relationship, the angle is the effect, i.e. the result. What is(are) the cause(s)?

17 Two Pulley System How much force is required to lift a 52-kg box at constant velocity with a twopulley system?

18 Four Pulley System

19 Static Connected Objects What are the forces in these two cases?

20 Pulling Connected Objects When forces are exerted on connected objects, their accelerations are the same. If there are two objects connected by a string, and we know the force and the masses, we can find the acceleration and the tension:

21 Pulling Connected Objects We treat each box as a separate system:

22 Pushing Connected Objects: Contact Forces Since both objects have the same acceleration, F = (m 1 +m 2 )a. However in the top case F 21 =m 1 a, while in the bottom case F 12 =m 2 a. Note the middle box may get crushed.

23 Pulling Connected Objects If there is a pulley, it is easiest to have the coordinate system follow the string:

24 Counter-weights Atwood Machine Elevator Pulleys and Springs Garage Door Opener Compound Bow

25 Falling Ball Chain Demonstration

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