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
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 quarterpound 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.
Fw = mg
= (50 kg)(9.8 N / kg)
= 490 N (newtons)
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.
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?
2. With a small force, stretch the paper
spring slightly.
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) 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
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:
Fw = mg
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.
 1 kg  
N
= (100 g ) 
9.8 


kg 
 1000 g  
= 0.98 N
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.
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.
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.
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.)
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