Newton’s Laws
1.
Force law of a Spring.
A. What we want to do is find out how the force
exerted by a spring depends on how much it is stretched. Call m the mass and x the amount of stretch
(call x = 0 the point when there are no masses on the mass-holder). Hang different masses m from the spring and
measure its stretch. Make a table of m
and x. The force F exerted by the
spring is equal to the weight of the mass m, since the mass is in
equilibrium. The weight of the mass is
mg, where g = 9.8 m/s2 as usual.
Add a third column to your table to show F (i.e., mg). Then plot F versus x. Do you get a straight line? If so, find its slope. If not, check with me! An ideal spring satisfies the force law F =
kx. “k” is known as the force constant
of the spring. What value do you find
for k?
m x F (=mg)
F
x
B. Suppose
you had two springs side by side. Would
this combination have the same effect as a single spring, or would it act like
a spring of force constant “2k?”
“k/2?”
Make a prediction, and then try it out.
C. Suppose
you attached two springs end to end.
What would the effective spring constant for this combination be? Make a prediction first, and then try it to
find out.
2. Free
body diagrams.
Draw
free body diagrams for the following situations.
a. A mass sliding down a frictionless inclined
plane.
b. A car moving down the road at constant speed
in a straight line.
c. A car going around the corner.
d. A car is pushing a truck. Draw free body diagrams for both the car and
the truck.
e. A block is being pulled across the table by
a string which is attached to the block.
3. Air
resistance.
As a body moves through the air, the air exerts a
force on that body which opposes the motion.
This force is just due to the molecules of air hitting the body. The
force of air resistance (which I'll call R) increases in strength as the speed
of the object increases. It might look
something like this:
R
v
Sketch a graph of the acceleration of a
falling body as it falls through the air.
a
v
If
the acceleration in the graph above is decreasing, does it appear to go through
zero?________ If it is not decreasing, you'd better talk to
your neighbor or your instructor.
Next
sketch a plot of the speed of this falling body as a function
of time...this is just a schematic, since you don't have enough information to
draw an accurate graph.
v
t
State
in words what your analysis has concluded about this situation. To aid in your explanation, answer the
following: Two objects are identical
except that one is more massive than the other. If these two objects are dropped
simultaneously from an airplane at high altitude, which will hit the ground
first?
4. A
force problem:
Two blocks are connected by a
string, and a second string attached to the right-most block is pulled to the
right with a force of 50 N. What is the
acceleration of this system?
[Hint: treat the two blocks as a
single body] There is no friction.
50N
4 kg 6 kg
What
is the tension in the string joining the two blocks? [Hint: draw a free body
diagram for the 4 kg block.]
5. Newton’s third law and Transportation.
Blow
up a balloon and let it go. How does
this demonstrate the third law? The
balloon is similar to a rocket in its use of action-reaction to propel itself. Think about other forms of
transportation. Make a list of
different types, and tell how action-reaction makes the vehicle go…unless you
think you have found an example that is not
propelled as a result of
action-reaction. List at least 5 different forms of transportation.
i.
ii.
iii.
iv.
v.
6. A woman is shopping at a shoe store. While she is looking, a box of shoes falls
from a shelf above her and hits her on the top of her head. She subsequently experiences neck pains and
sues the store. The defense lawyers
claim that the box, which weighs a mere 2 pounds, could thus only exert a force
of 2 pounds on her head, and 2 pounds is too little a force to do her any
harm. As lawyer for the woman, what do
you say?