need help with physics lab report

NORTHERN ILLINOIS UNIVERSITY

PHYSICS DEPARTMENT

Physics 253 – Basic Mechanics Fall 2016

Lab #8

Lab Writeup Due: Mon/Tue/Wed/Thu, Oct. 17/18/19/20, 2016

Read Giancoli: Chapter 5 (Lecture Notes #8)

Centripetal Force

Apparatus

This experiment uses a vertical shaft that can freely rotate to spin a massive bob

of mass m . The bob hangs by two strings from a horizontal bar with a counterweight on the other side. The counterweight helps the shaft rotate evenly. A spring connects the

bob to the shaft and provides a force to pull the hanging mass toward the shaft.

A vertical indicator is used to line up the bob. When the spring is not connected

to the bob, the bob should hang directly over the indicator. A string can be connected

from the bob over a pulley at the end of the apparatus to a hanging weight. The weight is

used to measure the spring force when the shaft is not rotating.

When the weight is disconnected from the bob, the shaft can be spun by hand. As

the shaft spins, the mass will swing away from the shaft held back by the spring. With

enough rotational speed, the mass will line up directly over a vertical post. A clock is

used to measure the number of revolutions, n , in a time, T , for the spinning bob.

Theory

Force, acceleration and velocity are all vectors. This means that they have both a

magnitude and a direction. Acceleration occurs when velocity changes in magnitude or

direction over time. Because velocity is a vector, even if the speed is constant the

velocity can still change due to a change in direction. A car accelerates as it goes around

a curve even though its speed is not changing.

Uniform circular motion occurs when an object moves in a circular path at a

constant speedv . The speed of the object moving in a circle can be determined by the angular speed  times the radius, r , of the circle. The angular speed is the number of rotations n an object makes times  2 radians divided by the time T it takes to make the n revolutions. Thus,

2 nr

v r T

   (1)

For uniform circular motion the acceleration is always pointed towards the center

of the circle. This acceleration is called centripetal acceleration. The magnitude of the

centripetal acceleration c a is 2v r or using Eq. (1) for the speed v :

2 2 2

2

4 c

v n r a

r T

   (2)

A net force on an object gives rise to an acceleration of that object. The

acceleration is in the same direction as the force and has a magnitude equal to the net

force divided by the mass of the object. Since an object in uniform circular motion has

an inward pointing acceleration, it must also have an inward pointing force (called a

centripetal force). That inward pointing force comes from the stretched spring exerting a

spring force tending to pull the spring back together:

2 2

2

4 s c

mn r F ma

T

   (3)

The force exerted by the spring is balanced by an equal and opposite gravitational force

from the massM hanging from the pulley. The inward-directed force of the spring is then

s g F F Mg  (4)

Data Collection

(1) Measure the mass, m , of the bob, and the diameter, d , of the vertical shaft and write

down these values and their uncertainties in your lab notebook.

(2) Slide the indicator bar to the closest position and measure the distance from the shaft

to the indicator and add half the diameter 2/d . This total is the radius, r , of its circular path.

(3) With the spring disconnected from the weight, adjust the knob on the top of the horizontal bar so that the bob hangs directly over the indicator. Re-attach the spring

and tighten all screws.

(4) Attach the string to the pulley and hanging mass.

(5) Add weight to the hanging mass until the bob is directly over the indicator. Record the total hanging mass M and its uncertainty.

(6) Practice rotating the vertical shaft pulling so that the bob moves to consistently pass over the indicator. Hold a white sheet of paper behind the indicator to see the bob

and indicator tips more easily.

(7) When you feel that you can do this, measure the time T it takes for the bob to make 50 revolutions ( 50n  ) using the photogate detector (fix the position of the photogate so that it is over the knob at the top of the horizontal revolving bar).

Notice that the photogate detector double counts. That is, it measures both when the

bob enters the photogate detector and (a very short time later) when the bob leaves

the detector. Thus, to get the proper number of revolutions, divide the number of

measurements the computer makes by a factor of 2 to get the proper value of n . Repeat this 5 more times and record the results. Find the average value of the 6

values for T and its uncertainty by calculating the standard error of the mean.

(8) Slide the indicator bar to the middle position. Measure the radius r as in step 2.

(9) Repeat steps 3 through 7 for the new position finding M and T .

(10) Slide the indicator bar to the end position (this will give you 3 different r values). Measure the radius r as in step 2.

(11) Repeat steps 3 through 7 for the new position finding M and T .

Analysis

(1) Use Eq. (3) to find the spring force (which is equal to the centripetal force) s F in

Newtons. Determine your uncertainty in this value using the method of propagation

errors (assume there is no uncertainty in the value n ).

(2) Use Eq. (4) and M from step 5 to find the spring force s F in Newtons and its

uncertainty using the method of propagation errors.

(3) Compare your two measured spring forces by computing the percent difference:

 12

1 2 100

1 2

# # %

# #

measurement measurement Difference

measurement measurement

  



Note that we must use the “percent difference” relationship (rather than the “percent

error” described in Lab#4) because neither measurement is a commonly accepted

value of the spring force. Discuss your results.

(4) Repeat these comparisons for the other values of r . Does the centripetal force agree with the spring force to within your uncertainties? Where do the discrepancies come

from (that is, what are the possible sources of error?).

Due at the beginning of the next lab: a lab writeup (a Word document) uploaded to

Blackboard. Show your propagation error formulas in your writeup.