Download Investigation 5

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Investigation 5
Gravitation and Energy
Gravitation:
1.
What weighs more, one kilogram of lead or one kilogram of feathers? Explain.
2.
a.
How much do you weigh? Express your weight in pounds.
b.
Write your weight in Newtons, by multiplying your weight in pounds by 4.45.
c.
Now calculate your mass in kilograms. (Remember how mass and weight are related to each
other.)
d.
The force the earth exerts on you as calculated by using Newton’s Universal Law of Gravitation
m m
is G 1 2 2 , where G = 6.67 x 10-11 N m2/kg2, m1 = mass of earth = 5.98 x 1024 kg, m2 = your mass
d
in kg, and d = radius of the earth = 6.378 x 106 m. Should the value of this force be the same as
the value of your weight found in part b? Explain.
e.
The gravitational force on objects on the surface of the moon is approximately 1/6 of the
gravitational force the earth exerts on the same objects.
1)
What is the value of your mass when you are on the moon?
2)
How much do you weigh on the moon?
3.
4.
A physics student weighs 120 lb at the surface of the earth. Find her weight at the following
positions:
a.
a distance above the surface of the earth equal to the radius of the earth.
b.
a distance above the surface of the earth equal to four times the radius of the earth.
c.
at the center of the earth.
a.
What is the shape of the orbit in which the earth is traveling around the sun?
b.
At what point in its orbit around the sun is the earth traveling the fastest?
Energy and Work:
1.
Write your mass in kilograms _________________ kg
2.
When you climb stairs, you are doing work lifting your body upward against the gravitational force.
The force needed to lift you at a constant velocity is equal to your weight (remember w = mg). Now
calculate the work you do in climbing stairs (remember that the work done is the force times the
distance you move the object (yourself) in the direction of the force (up).
The approximate height of the staircase outside our lab is _________ m.
a.
If you were to climb the stairs, then how much work would you do?
_______________ Joules
3.
Time yourself climbing the stairs. You can do it rapidly, slowly, or at any speed you choose. But no
matter how you do it, hold onto the railing. The time is
_____________ seconds
4.
Now find your power output while you were climbing the stairs.
Power output 
work done in Joules
time in seconds
_____________
Joules
or Watts
sec
How does your power output compare to a 100 Watt lightbulb?
5.
This value can also be expressed in horsepower. Divide the power output in Watts by 746 to get
horsepower.
______________ hp
How does your power output compare to a horse’s power output?
Conservation of Energy
We know that energy can neither be created nor destroyed, but it can be converted from one form to
another.
Suppose a 1 kg ball is at the top of a 40 meter high cliff. In the first case, at position A, we drop the ball
and in the second case we throw the ball downward so that it leaves our hand at 10 m/s. Position D is
just before the ball hits the ground. Take the acceleration due to gravity to be 9.8 m/s 2.
1.
The 1 kg ball weighs ______________ Newtons.
2.
Complete the table below. Make as few calculations as possible. Keep in mind the idea of
Conservation of energy. Notice that the gravitational potential energy is zero at position D.
A
10 m
B
position
ball dropped
10 m
gravitational
potential
energy
(Joules)
kinetic
energy
(Joules)
ball thrown downward at 10 m/s
total
mechanical
energy
(Joules)
gravitational
potential
energy
(Joules)
kinetic
energy
(Joules)
total
mechanical
energy
(Joules)
A
C
B
C
20 m
D
0
0
D
3.
After the ball hits the ground its gravitational potential energy is zero, its kinetic energy is zero,
and therefore its total mechanical energy is zero. So what happened to all the energy?