4.2. The Normal Force, Apparent Weight and Hooke s Law

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1 4.2. The Normal Force, Apparent Weight and Hooke s Law

2 Weight The weight of an object on the Earth s surface is the gravitational force exerted on it by the Earth. When you weigh yourself, the scale gives a measurement of the pull of Earth s gravity. On the moon, your weight (but not mass) would be less.

3 Force Direction: Normal Forces The force exerted perpendicular to the surface of contact between any two objects is called the normal force. In mathematics, normal means perpendicular.

4 Force Direction: Normal Forces The origin of the normal force is the interaction (bonds and repulsion) between atoms in a solid that act to resist deformation of the solid. When a can of soup is placed on a countertop, it does cause a very small compression of that surface. The greater the mass placed on the countertop, the greater the normal force the countertop exerts to oppose being compressed. A solid behaves like a very stiff spring on the molecular level.

5 Normal Forces The normal force may be equal to, greater than, or less than the weight. ΣF y = N W F 1 sin 60 F 2 sin 30 = 0 N = W + F 1 sin 60 + F 2 sin 30

6 Normal Forces The normal force is always perpendicular to the surface.

Weight and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there?

7 Weight and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? The normal force exerted by the table is exactly as large as needed to balance the weight of the object. It is a reaction force. If the weight of the statue is larger than the normal force that can be supplied by the table s molecular bonds, the table breaks!

8 Example You pull a 19-kg suitcase with a force of 21 N at an angle of 31º. (a) What is the normal force exerted by the floor on the suitcase? (b) If your velocity is constant, what is the force of friction on the suitcase?

9 Answer

10 Apparent Weight Your perception of your weight is based on the contact forces between your body and your surroundings. If your surroundings are accelerating down or up, your apparent weight---the normal force of the floor on you, W a ---will be more or less than your actual weight. ΣF = W a W = ma W a = W + ma = mg + ma

11 Apparent Weight W a = mg + ma In free fall (a = -g), you feel weightless. You also feel weightless in outer space, where g 0, if there is no acceleration. A pilot or astronaut feels additional G s when accelerating.

12 Example Your mass is 69 kg. 1. What is your weight on a scale in N? F = mg = (69 kg)(9.80 m/s 2 ) = 680 N 2. You are standing on a scale in an elevator accelerating upward at 1.0 m/s 2. What does the scale read (in N)? W a = mg + ma = (69 kg)(9.8 m/s 2 ) + (69 kg)(1.0 m/s 2 ) = 750 N

13 Your mass is 69 kg. Example 3. You are standing on a scale in an elevator accelerating downward at 1.0 m/s 2. What does the scale read (in N)? W a = mg + ma = (69 kg)(9.8 m/s 2 ) + (69 kg)(-1.0 m/s 2 ) = 610 N 4. You are standing on a scale in an elevator moving upward at constant velocity. What does the scale read (in N)? W a = mg + ma = (69 kg)(9.80 m/s 2 ) + 0 = 680 N

14 Demonstration Put a 1-kg mass on a demonstration spring scale and observe the readings when the mass is 1. stationary 2. accelerating up 3. accelerating down 4. moving with constant vertical velocity

15 Springs Springs are useful because they exert a restoring force when stretched or compressed. Hooke s Law states that a spring s force increases linearly with the length the spring is stretched or compressed: F = k x The constant k is called the spring constant. The larger k is, the smaller the x for a given F. Similarly, the more force you pull a spring with, the farther it will stretch.

16 Springs Hooke s Law: F = k x This is why the gradations on a spring scale are spaced evenly. What are the SI units of the spring constant, k? Note that Hooke s Law is not a law of nature (like F = ma), but a good empirical approximation for real springs that aren t stretched too far (beyond which they become permanently deformed).

17 Example Hooke s Law: F = k x

18 Mini-Lab 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?

Force mediated by a field - long range: action at a distance: The attractive or repulsion between two stationary charged objects.

Force mediated by a field - long range: action at a distance: The attractive or repulsion between two stationary charged objects. VISUAL PHYSICS ONLINE DYNAMICS TYPES O ORCES 1 Electrostatic force orce mediated by a field - long range: action at a distance: The attractive or repulsion between two stationary charged objects. AB A