Section 5 Hooke’s Law: Finding Your “At Rest” Weight

2. In physics, weight is defined as the force of gravity on an object. The weight (force) is the mass of an object multiplied by the strength of the gravitational field at the location of the object. Large masses are heavy (have large weights) and small masses are light. In the metric system, the mass of an object is measured in kilograms. The strength of the gravitational field near the surface of Earth is 9.8 N/kg (newtons per kilogram). The unit newton per kilogram is equivalent to meters per second every second. Using this information, you can calculate a student’s weight (force). The student has a mass of 50 kg.

weight (force) = mass strength of×

gravitational field

wF mg=

= ( )( . / )50 9 8kg N kg

= 490 N (newtons)

The unit for weight is the newton (N). Weight is a force and has the same units as any other force.

a) Calculate and compare the weights of a gymnast with a mass of 40 kg and a football player with a mass of 110 kg.

3. On the surface of the Moon, the strength of the gravitational field is only about 1.6 N/kg.

a) What would be the weights of the gymnast and the football player in Step 2.a) if they were on the Moon?

4. The newton is the metric unit for weight. However, you may wish to compare this to a pound, with which you are more familiar. Each kilogram (mass) has a weight of 2.2 lb on Earth. A 220-lb football player has a mass of 100 kg. The weight (force) exerted on 100 kg, according to the equation Fw = mg, is 980 N.

a) Find the weight in newtons of a bowling ball that weighs 11 lb.

b) Find the weight in newtons of a ¼-lb burger (a patty that has a weight of ¼-lb).

5. The weight of a ¼-lb burger is close to 1 N. In a country that uses metric measurements, a restaurant could call their ¼-lb burger a “Newton Burger.” You can use this as an approximate way to determine how much something weighs in newtons if you know the weight in pounds. A 50-lb person has the equivalent weight of 200 quarter-pound burgers (200 × ¼-lb). Therefore, the 50-lb person has an approximate weight of 200 N.

a) Using this technique, find the approximate weight in newtons of a roller-coaster car that weighs 1500 lb.

Part B: The Properties of Springs

1. Make a spring from a piece of paper. Take a piece of 8½ × 11 paper. Fold it like an accordion.

2. With a small force, stretch the paper spring slightly.

a) Record what happens when you release the paper.

3. With a small force, compress the paper spring slightly.

a) Record what happens when you release the paper.

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Chapter 4 Thrills and Chills

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Chapter 4 Thrills and Chills

4. Does the paper spring return to its original size and shape as the force of the stretch increases? Try it.

a) Record your observations.

5. A metal spring has properties like those of the paper spring. The metal spring is usually better able to restore itself to its original shape than the paper spring. However, the metal spring can also be stretched past its load limit so you should be careful not to do this.

6. The stretch of a metal spring can be measured precisely. You can use a set of masses to determine the properties of springs. Secure the spring vertically as indicated in the diagram. Attach a metric ruler to the ring stand or support holding the spring. Use a file card to note the bottom-most position of the spring. Set this measurement as the zero measurement for the stretch of the spring. You are now ready to measure the stretch of the spring with a given set of masses.

You may have to convert from grams to kilograms to newtons. If a 100-g mass is used, this is equivalent to 0.1 kg. The mass of 0.1 kg has a weight of 0.98 N. This can be written as a single equation:

F mgw

gkg

gNkg

N

=

=⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

=

( ) .

.

1001

10009 8

0 98

Notice that you converted grams to kilograms by multiplying by 1 kg/1000 g. In math class, you learned that you could always multiply a number by 1 and not change its value. For instance, 27 × 1 = 27. Since 1 kg is equal to 1000 g, the fraction 1 kg/1000 g has an equivalent numerator and denominator and the fraction equals 1.When you use this fraction in the equation, the 100 g-mass gets converted to 0.1 kg. The gram units “cancel” and you are left with kilogram units. This unit conversion was done because you want the mass in kilograms.

a) In your Active Physics log, create a data table with four columns. Label the first three columns mass, weight (of the mass hung on the spring), and stretch of spring. The fourth column will be left blank for the time being.

7. Measure the stretch of the spring (from its “relaxed” or zero position length to its stretched length) for different masses.

a) Record your measurements in the data table.

b) Plot a graph with the stretch of the spring on the x-axis and the weight on the y-axis. (Keep in mind that this is a bit unconventional since the independent variable is usually placed on the x-axis.)

Be careful when placing and removing masses so that the spring does not snap and hurt anyone. Have one person hold the bottom and top of the spring as another person adds or removes each mass.

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