Spring 2007 Name______________________
Physical
Science Lab
Centripetal
Force
Uniform
Circular Motion
Objective: To study the forces necessary to maintain
uniform circular motion and to confirm the equation for centripetal motion.
Complete
questions 1-5 before coming to class.
You will need to read the entire experiment to do this (as well as read
pages 48-50 in your text).
1)
Write the equation, which is used to calculate the centripetal force.
F =
2)
Explain what each of the following (used in the formula in question 1)
represents. Place the correct units
for measuring each of these in parentheses at the end of your answer.
a) r = b) m = c) F =
d) v =
3)
Calculate the centripetal force of an object of mass 0.7 kg rotating with a
speed of 4 m/s at a radius of 0.5 m.
F =
Write the equation for
calculating the circumference of a circle. (If you don’t remember, read the
lab.)
C =
When
a ball on the end of a string is swung in a vertical circle, if the ball
travels too slowly, it will not complete the circle. To make the circle the gravitational force
must equal the centripetal force. Write
the equation for the force of gravity (weight) of an object of mass m. Use the gravitational constant g in your
formula.
W =
(4)
Now set this equation equal to the centripetal force as you wrote it in
question 1, and solve the equation for the velocity of the object. Clearly show each step of the solution.
W = F v
=
How
fast must an object be swung in a vertical circle to keep the string tight at
the top if the radius of the circle is .5 m?
Clearly show your work.
v =
(5)
Copy this answer to part 14 of this lab.
Mark an “x” when copied.____
Note:
There is only one apparatus for the first part of this experiment, so everyone
in the lab will work together, with different people doing various steps of the
experiment.
Method:
The apparatus consists of a weight on a spring, which is rapidly rotated. As
the weight and the spring rotate, the spring is stretched. The speed of rotation
necessary to maintain the weight in position is measured. Weights are then hung
on the spring to determine the amount of force necessary to stretch the spring
the same amount as when it was rotating. This force is then compared to the
centripetal force as determined by the equation in question 2.
6)
To use the equation for centripetal force (question 2) we need know three
things: a) the mass of the rotating
weight, b) the speed (velocity) with which it is moving, and c) its mass. The
mass has already been measured and is marked on the apparatus, the mass is
m = _______________ g = _________________ kg.
7)
To measure the velocity, we will first determine how many revolutions the
apparatus makes in a known amount of time, determine how far it has gone during
that time, then use the v=d/t equation to determine the velocity. The first
step is to make sure the rotational velocity is a constant as possible and that
the apparatus is rotating just fast enough to produce the centripetal force
necessary to stretch the spring a known amount. To do this we will count the
number of revolutions in 30 sec. Everyone in the class will do this. Then we
will take an average. Results that are
quite different from the rest of the data will not be included in the average.
Revolutions in 30 seconds
1. ________________ 8. ________________ 15._____________
2. ________________ 9._________________ 16._____________
3. ________________ 10.________________ 17._____________
4. ________________ 11.________________ 18._____________
5. ________________ 12.________________
19._____________
6. ________________ 13.________________ 20._____________
7. ________________ 14.________________
21._____________
Ave
= ____________________
8)
To determine how far the mass traveled in 30 sec., we will first calculate the
distance the center of the mass travels in one revolution, then multiply by the
number of revolutions. You may remember the circumference (the distance around)
a circle is 2πR, where π = 3.14 and R is the radius of a circle. To
measure R, we hang the apparatus by one end and stretch the spring the amount
necessary to make the pointer move to the same position as when rotating.
Vernier Calipers are used to measure the distance.
R = ___________________ cm =
______________________ m
Distance traveled in one rotation = 2πR =
Distance traveled in 30 sec. =
Velocity = distance/time =
9)
Calculation of Centripetal force using the equation
F = (mv2)/R (label all units correctly!)
Mass
= _____________, R =
________________ V = _____________
F = (__________) x (___________)2 / (__________) =
_________
10)
To check our results, we now determine the amount of mass necessary to stretch
the spring and calculate the weight of this mass.
Total mass on spring = _______________g =
_______________kg
F = ma, W = mg =(_______________)x(9.8 m/s2) =_____________
(mass) (weight)
11)
The calculation of the percent error will give a quantitative measure of the
agreement of the two answers. This is
calculated by:
(answer 10) - (answer 9)
answer 10 x 100 = percent
error
In our case this is (Show your work):
% diff = ____________________________________ =
[ ]
12)
List what you believe could be some of the causes of error in this experiment
and tell how you think the results could be improved.
13)
Gravity versus centripetal force.
You will swing a tennis ball on the end of a
string just fast enough to keep it going in a vertical circle. Your partner will time the number of
revolutions in 15 sec. You will then use
the equations you developed on the front page to do the calculations.
14)
Copy from first page of your lab: equation for v =
Use
this equation to calculate the velocity necessary to keep a ball on a .5 m
circle.
(a) v
=
Take
one of the tennis balls connected to a string and measure a distance from the
center of the ball to 50 cm up the string.
Twirl
the ball in a vertical circle with a radius of 50 cm as slow as it will go and
stay on the circle (the string should not go slack).
Number
of revolutions in 15 seconds = ___________
Calculate
the distance around a 50 cm radius circle = 2πr =___________
(Be
sure your answer is in meters)
15)
Velocity = d/t=total distance traveled in 15 sec/15sec =
The
velocities calculated in items 14) and 15) are actually quite different. The velocity in item 16 is at the top of the
circle, and that of item 14) is the average velocity. Gravity makes the ball speed up as it falls
and slow down at the top of the circle.
To compensate for the difference we will calculate the velocity of an
object that falls one meter (the distance the ball falls each revolution.)
Use
the following equation with h = 1 meter.
16)
Velocity of an object after falling a height h is given by: v = 
=
17)
The average velocity will be half this value or ________________ m/s
To
compare your result to the calculated value in item 15 you should subtract the
average velocity calculated in item 18.
Experimental
result = velocity from item 15 - velocity from item 17
18) Experimental result =
Calculate
the percent error
Item 18 -
Item 14(a)
Experimental result - calculated result
= __________________ = %
Calculated result
Item 14
Tell
what you believe to be the most important thing you learned in this experiment.
If
any part of the experiment is unclear, what is it?