CONSTANT FORCE AND CHANGING MASS
The amount of an object’s acceleration depends on the _____ (inertia) of the object and the size of the ______ acting on the
object. In this lab a car will be pulled by a mass (through a pulley). The pulling mass (or pulling force) will be held constant.
Since the force acting on the car is constant, it is called a ___________ variable. You will change the mass of the car
and you will observe how the resulting acceleration of the car. The mass of the car is the independent variable or ________
variable. The acceleration is the dependent variable or __________ variable.
So the purpose of this lab is to investigate the effect of increasing ______ in an accelerating system.
What do you think ? as the mass increases, you expect the acceleration to ________ .
You will derive Newton's second law: _______.
MATERIALS: small cart masses meter sticks time watch pulley C-clamps
masking tape string masses graph paper.
PROCEDURE
Step0: find the mass of the car using a spring scale. Mass car = ____________ g (hang the car on the spring scale)
Step1: Fasten a pulley over the edge of the table or the track. The pulley will change the direction of the force from a downward pull on the pass into a sideways pull on the cart.
Step2: (see picture) Tie one end of the string to the cart and thread it over the pulley.
Add a 5g holder to the other end of the string so that when the cart is pushed slightly it moves at a constant speed.
Mark off a distance on the track top slightly shorter than the distance the mass can fall from the table to the floor.
(GIVE ME A BREAK, STOP THE CART BEFORE IT CRASHES INTO THE PULLEY)
Step3: Add 5 masses of 100g to the cart. It may be necessary to secure the masses with masking tape.
Step4: Practice accelerating the cart a few minutes to ensure proper alignment.
Add a 20g mass to the mass holder. KEEP THIS FALLING WEIGHT THE SAME AT ALL TIME.
M total mass moving the car = mass holder + 20 grams = __________ g stays constant = _________kg
The weight of this mass M will be the force F pulling the car. This force F is a ___________ variable.
F = _______ N (weight = mass(kg) x 10 , you should know that by now ! )
Step5. Time the motion. You can use stop watch or the computer (stopwatch on-line)
Repeat 4 times and record the data in table 1.
| mass in car m | time 1(s) | time 2(s) | time3(s) | time4(s) | average time (s) | acceleration (1/s2) = 1/t2 |
| 500g | ||||||
| 400g | ||||||
| 300g | ||||||
| 200g | ||||||
| 100g |
Step 7: Use the average times for each mass from steps 5 and 6 to compute the acceleration of the system.
You will learn later one that when the acceleration if a system is constant (the speed increases at the same rate and keeps the same direction)
then , there is a simple relationship between the distance d covered by the accelerating system (the car) , the time t it takes the system (car)
to cover the distance d and the acceleration a of the car. We have d = 0.5 a t2. So a = 2d/t2.
just checking if you take the time to read over the lab: :-)
d is _____________ covered by the car, t is the _______ it takes the car to cover ____________ d and a is the _____________.
Since the cart always accelerates through the same distance d , the acceleration is proportional to 1/t2. Simply calculate 1 /t2 and make 1/(second)2 your unit of acceleration. Record the data in the table and complete the table.
ANALYSIS
1) : Graph acceleration(y) vs mass (x) (you can use the TI to give you an idea what the graph should look like, ask me if you forgot).
YOU SHOULD NOT GET A LINE !!! YOU SHOULD GET A CURVE !!! don't forget the title
and don't forget the label the axis with the right units.
2) The graph shows that as the mass increases, the acceleration ________________.
3) Your graph shows an inverse relationship between the ____________ and the ___________. y = b / x
with y is the __________ and x is the _______________. You know that F = m a . So if y is the acceleration
and if x the the mass, what is b ? __________________
4) The relationship between mass and acceleration tells you if you double the mass, the acceleration is _________________.
We say the acceleration is ________________ proportional to the mass.
5) EXTRA CREDITS - MORE ADVANCED. In our graph y = acceleration and x = time.
Let's try to find the best equation that fits the data. You know that a = F / m with F constant (same weight was pulling the car,
same force was accelerating the car) or y = b / x . You can also write y = b x-1 . This is a power function.
Goto STAT CALC and find the best-fit relationship for your data. (remember it is a power function)
The equation is ________________ (acceleration = ____ / mass) you have b=___________.
b is a constant and only depends on the __________ you place on the holder. It is the unbalanced _________ that accelerates the car.
We say the acceleration is ____________ proportional to the mass. If the mass is doubles, the acceleration is ___________ by 2.
ANALYSIS
GOING FURTHER
I) A group of students collected the data below:
| x= acceleration (m/s2) | y = force (kg m/s2 or N ) |
| 0 | 0 |
| 6 | 10 |
| 12 | 20 |
| 18 | 30 |
| 24 | 40 |
1) graph these data. Don’t forget to label the axes and title the graph.
(you don't need the TI).
2) Describe the relationship between force and acceleration as shown by the graph.
(linear (y=mx)? Inverse (y=m/x) ? Quadratic (y=mx2) ? )
3) What is the slope of the graph? Remember to include units with your slope.
(unit for y is kg m/s2 and for x is m/s2 , slope is change in y over change in x)
slope = _____ ____ units are _______
4) What physical quantity the slope represent ? (look at the units)
5) . Write an equation for the line. (y = m x and m is the slope)
6) The graph shows that the force is ______________ to the acceleration
7) You just found Newton’s second law ______________
8) When the acceleration increases by 6 m/s/s, the force increases by __________N
9) What is the acceleration when the force is 50.0N ?
10) What is the value of the force for an acceleration of 15m/s2?
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