Download Newton`s Second Law Purpose: Investigate Newton`s Second Law

Newton’s Second Law
Purpose: Investigate Newton’s Second Law of Motion
Concept and Skill Check
Newton’s second law of motion states that the acceleration of a system is directly proportional
to the net force on it and inversely proportional to its mass. In mathematical form, this law is
expressed as a= F/m. An object will accelerate if it has a (net external) force acting on it, and
the acceleration will be in the direction of the force. In this experiment, a laboratory cart will
be accelerated by a known force, and its acceleration will be measured using a motion sensor
and computer. The product of the total mass accelerated and its acceleration equals the force
causing the acceleration.
In order to calculate the net force acting on the laboratory cart, frictional forces that oppose
the motion must be offset. If the cart moves at a constant velocity, then the net force acting on
the cart is zero because the acceleration is zero. The frictional force can be neutralized by
providing enough small masses at the end of the string to make the cart move forward at a
constant velocity. If you assume that the laboratory cart experiences a uniform acceleration
due to the falling mass, then the relation ship
d = vit + ½ a t2
applies. If the cart has an initial velocity of zero, the equation becomes
d = ½ a t2
If the displacement in a given time is known, you can solve for the acceleration with
a = 2 d/t2
Materials
Computer, Motion sensor , Data Studio software, mass sets with hangers and paper clips for
fine mass adjustments, heavy string (1.5m), triple beam balance, dynamics cart, track, meter
stick or track with measurements for distance.
Procedure
1. Determine the combined mass of your dynamics cart and string and any masses riding
on top of the cart. Record the mass in Table 1.
2. Assemble the cart, pulley, motion sensor as shown in Figure 1 on the next page.
(Modifications will be made if your equipment is different than the picture.) Tie a small
loop in the end of the string hanging from the pulley.
3. Give the cart a small push. It should roll to a stop in a few centimeters. Attach a small
mass (paper clips or plastic “hanger assembly”) to the end of the string that is hanging
from the pulley. Give the cart a small push toward the pulley and observe its motion. If
the cart moves a constant velocity then the weight of the mass is equal to the force of
friction in the cart’s wheels and from the any other sources of friction. If the cart rolled
to a stop, then the total mass on the string must be increased. If the cart’s velocity
increased after it was released, then the total mass on the string must be decreased.
Adjust the total mass until the cart moves a constant velocity after you have given it a
small push. Record in Table 1 the mass needed to equalize the friction of the cart.
Leave the small masses attached to the string. Take a screen shot of your computer
using the Print Screen function or the Snipping Tool to submit with your lab.
4. Now you are ready to accelerate the system. Start by adding about 50 grams to the
hanging mass that you just used to neutralize the friction in the system. Record the
total of these masses in Table 2 under Trial 1.
Determine acceleration with two methods. You should perform these as the same time.
In the first, use DATA Studio to determine the acceleration of the system. Move the cart
next to the motion sensor. Adjust the string length so that the mass is hanging just
under the pulley. Hold the cart to prevent it from moving. Turn on the motion sensor.
Release the cart, allowing it to accelerate across the track. Catch the cart before it
collides with the pulley or plunges to the floor. Turn off the motion sensor. Record your
data in table 3.
For the second method use a stop watch and the formulas described at the beginning of
the lab. Record your values in Table 4. Calculate the acceleration and compare it to
that of the computer.
5. Repeat steps 5 and 6 twice more for a total of three trials. Use different masses for
different accelerations of the system. Do not exceed 150 grams.
Observations and Data
Table 1
Value (kg)
Mass of laboratory cart with any riding
weights
Mass needed to equalize friction of cart
Force of Friction (N)
Table 2
Trial
Hanging Mass
(kg)
Accelerating
force (N)
Force of Friction (N)
From table 1
FNET (N)
1
2
3
Table 3
Trial
Mass of laboratory
cart with any riding
weights from table 1
(kg)
Hanging Mass
from table 2
(kg)
Total mass of
system (kg)
Acceleration
calculated by
computer
(m/s2)
1
2
3
Table 4
Trial
1
2
3
Total mass of
system (kg) from
table 3
Stop watch time
(s)
Displacement
(m)
Acceleration
calculated by you
(m/s2)
(msystem) *(a)
(N)
Analysis: All values that have been calculated and inserted into the above tables must be
shown here. Use a working equation, show algebra if relevant and finally substitutions and box
your final answers.
1. Show calculations for the frictional force along with a free body diagram of the cart.
This diagram refers to the cart moving at constant velocity. Forces are balanced or
said to be in equilibrium.
2. Show calculation for the accelerating force.
3. Why was it important to neutralize the effect of friction force acting on the system?
4. Are your acceleration values less than, equal to or greater than g? Are these the
values you would have predicted? Explain.
5. The total mass that was accelerated is equal to the mass of the cart, string, the riding
weights if you used them, the small masses need to equalize friction, and the hanging
mass. Calculate the total mass of your system and record this value in t Table 3
6. Calculate the product of the total mass and the acceleration for each trial using the
computers values of acceleration. Record these values in Table 3.
7. Calculate the product of the total mass and the acceleration for each trial using your
stopwatch-derived values of acceleration. Record these values in Table 4. Compare
the values and comment.
8. Compare the results for the product (m) (a) to the accelerating force. Find the relative
error using the accelerating force as the reference value.
9. Based on your answers for # eight. Have you succeeded in verifying Newton’s Second
law? Why or why not? Comment.
Application
At a specific engine rpm, an automobile engine provides a constant force that is applies to
the automobile. IF the car is traveling on a horizontal surface, does the car accelerate
when this force is applied? Explain.