Download Force and acceleration - University of Louisville Physics

Physics 111: Elementary Physics
Laboratory A
Force and Acceleration
1.
Introduction
The classic Greek philosopher Aristotle (circa 400 B.C.) observed that all terrestrial objects come
to rest unless they are acted upon by an external force. He thus related the effect of a force to the speed that
the object obtained when that force acted. This observation is so commonplace that it is often readily
accepted today, over 2000 years later. However, in the 17 th century an important correction was made by
Galileo regarding the relationship between a force and the state of motion of the object upon which the
force acts. He observed that if friction, the natural resistance to motion, could be reduced, a body would
stop more slowly, and he inferred that if the friction could be removed entirely, the state of motion of a
body would remain unchanged in the absence of other forces. He concluded that force is related not to the
speed of an object, but to the acceleration, the rate at which that speed changes. Galileo realized that
Aristotle’s observation should be corrected by noting that moving objects are brought to a stop by the effect
of a force of friction unless a second force is applied to counteract the friction. The tendency of a body in
motion to remain at the same speed in the absence of external forces is called inertia. The property of mass
is a measure of that inertia.
A few years after Galileo’s important observation, Isaac Newton made an observation, now known
as Newton’s Second Law which relates force, mass and acceleration:
F = ma ,
(1)
where F represents the net (total) force, including its direction, m represents the mass, and a represents the
acceleration, including the direction. This equation tells us that for a given net or unbalanced force, there
will be an acceleration in the direction of that unbalanced force with a magnitude which is inversely
proportional to the mass of the object on which the force acts. The greater the inertia of the object, the
smaller its acceleration will be, given the same force.
2.
Procedure
An air track apparatus will be used to let you measure the acceleration of a mass, and to find the
force exerted on the mass by gravity as the body is accelerated. The air track apparatus can be used to
achieve nearly frictionless motion. A cushion of air between the sled and the bearing surface makes
possible reproducible measurements as the sled slides down the inclined track under the influence of
gravity. You will find available an air track, a blower, a photogate timer, a balance, and a meter stick. The
end result of the experiment will be to calculate from Eq. (1) the force acting on a mass as it slides a
distance along the track. You will also determine directly the magnitude of the force and compare it
against the theoretical value from Eq. (1).
Acceleration is determined as the time rate of change of speed. If two speeds are determined a time
T apart, then a is the quotient of the change between the speeds, and the time T. In turn, a speed is the time
rate of change of distance. Thus by determining the time t needed for the sled to travel a distance d, the
speed is found by dividing: v equals the ratio d/t. The procedure will be to choose two intervals along the
air track, and to measure the speed of the sled in each interval. (These will actually be average speeds in
each case, but they will be good approximations to the speeds at the centers of the intervals if the intervals
are short.) A measurement of the time for the sled to pass from the midpoint of the higher interval to the
midpoint of the lower interval will give a value for T which you can then use to calculate the average
acceleration, the ratio of the change of speed to the time interval, ∆v/T.
The air track is sketched above. (The blower and the pipe have been omitted.) The first step in the
experiment is to determine the magnitude of the force which will cause the sled to accelerate down the
incline. The forces which act on the sled are the reaction force of the air track and the weight of the sled,
i.e. the force on the sled due to gravity. These forces
are sketched at the right. The reaction force, R, acts
perpendicularly upward from the air track to counter
the component of the weight, W, acting
perpendicularly to the track. Thus R equals Wcosθ,
where θ is the angle of inclination of the track. The
remaining, unbalanced component of W parallel to
the track has magnitude Wsinθ, and causes the
acceleration down the track.
Step by step instructions:
1.
Use a meter stick or caliper to measure the elevation, ∆h, of a length, L, along the air track. Record
these values and calculate sinθ.
2.
Use the balance to measure the mass, m, of the sled. Record m and calculate W, and find a value,
Fexp, for the accelerating force.
3.
In order to measure the lengths of the time intervals, t and T, you will use a pair of photogate timers.
An auxiliary timer is attached to a main timer by wires in a cable. The main timer is placed at the
upper end of the length along which the air track sled is to move, and the auxiliary timer is placed at
the lower end. The level of the timers is set so that the light beams in the timers will be broken as
the air track passes by. The main timer is set on the Pulse option. The time displayed on the main
timer is then the length of time between the instant the beam in the main timer is broken to the
instant when the beam in the auxiliary timer is broken.
4.
Choose the two short intervals along the air track which you will use for the measurement of the
acceleration. Record the lengths of each interval. Note that each interval must be larger than the
sled length. Record also the positions of the midpoints of each interval. (Take interval 1 to be the
higher one.) Use the timer to determine three values of the time needed for the sled to pass through
each interval, and record the average value below. Calculate v for each case.
5.
Place the timers at the midpoints of the two intervals and record three values of the time needed for
the sled to pass between these positions. Record the average value as T, and calculate a. Use the
value of the mass of the sled m, with your value for a to compute F theo, using Eq.1.
6.
Compare the magnitudes of F determined directly (in the first part of the experiment) and the
theoretical value (in the latter part of the experiment) by calculating the percentage difference
between them.
Physics 111: Elementary Physics
Pre-Lab Exercise
Force and Acceleration
Name: _____________________
Section: _______
1. Some typical data from this type of experiment are given below. Fill in the blanks .
Inclination:
∆h = 3.58 cm
Accelerating Force:
m = 37.8 gram
L = 1.00m
sinθ = ∆h/L = _______
W = mg = _______
Fexp = Wsinθ = _______
Time Intervals and Average Times:
Interval 1
Timer positions
35.0 cm
Interval 2
45.0 cm
Distance
85.0 cm
Time
95.0 cm
Avg time
Velocity
Interval 1.
________
0.183 s
0.189 s
0.185s
_______
v1= _______
Interval 2.
________
0.133 s
0.128 s
0.125s
_______
v2= _______
Time between midpoints:
0.751 s
0.757 s
0.752 s
Acceleration = (v2 – v1)/Tavg = __________
Tavg = _______
Ftheo = ma = __________
∆F(%) = 100[|(Fexp - Ftheo)|/Fexp] = __________
2.
Suppose you were able to measure all the quantities used in part 1 with unlimited accuracy. Would
you expect Ftheo and Fexp to be identical ? If not, why not ?
3. State briefly (100 words or less) the objectives of this experiment and the hypothesis which is to be
tested.
Physics 111: Elementary Physics
Lab Report
Force and Acceleration
Investigators:
________________________ ,
_______________________
________________________ ,
_______________________
________________________
Date: _____________
Procedure: Describe briefly (200 words or less) the procedures used in this experiment .
Data:
Inclination:
∆h =__________
Accelerating Force:
m = __________
sinθ = ∆h/L = __________
L =__________
W = mg = __________
Time Intervals and Average Times:
Interval 1
Timer positions:
__________
Distance
__________
Fexp = Wsinθ = __________
Interval 2
__________
Times
__________
Avg time
Velocity
Interval 1.
_______
_______
_______
_______
_______
v1 _______
Interval 2.
_______
_______
_______
_______
_______
v1 _______
_______
_______
_______
T = _______
Time between midpoints:
Acceleration = (v2 – v1)/T = ___________
Ftheo = ma = __________
∆F(%) = 100[|(Fexp - Ftheo)|/Fexp] = __________
Discussion: Does the comparison of Fexp and Ftheo support Newton’s Second Law ? Is the potential
accuracy of the experiment improved or reduced if the angle of inclination is increased ? Hint: think about
the measurement error in the times.