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Balanced Force Particle Model:
Review Sheet
1. a.
b.
c.
d.
e.
2. a.
b.
c.
d.
FT = Fg = mg = 49 N
FT = Fg/2 = 24.5 N
FT(bottom) = Fg = 4*g = 39.6 N FT (top) = Fg + 39.6 = 88.6 N
Fg = 60*9.8 = 588 N
Tension is more than weight because part of it (the vertical component) equals weight
e. Fg = 1000*9.8 = 9800 N
Normal force is less than the weight because part of the normal force and part of the
friction help counteract gravity
3. Consider a collision between a small car and a heavy truck. In such a collision, how does the
size of the force exerted on the car by the truck compare with the size of the force exerted on
the truck by the car? Explain your reasoning.
The size of the force of the truck on the small car is the same as the size of the force of the
small car on the truck. These two are a 3rd Law pair so they are equal and opposite.
©Modeling Instruction 2013
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U4 Freeparticle, review v3.1
4. a. Draw a velocity-time graph for a ball
thrown vertically into the air during its
up-and-down motion.
b. Draw a force diagram for the thrown ball
when it reaches its highest point.
FNet
Fg, b, e
c. At the highest point, is the velocity zero? Explain.
Yes, at the highest point the ball is not moving. Its velocity passes through zero as it
changes direction.
d. At the highest point, is the acceleration zero? Explain.
No, for the acceleration to be zero there must be a zero net force on the ball. The force of
the earth is always pulling the ball down. One can also say that the velocity is always
changing on the ball's trip, therefore it is always accelerating. A look at the graph above
shows that when the velocity is zero, the slope of the graph (acceleration) is not zero.
e. At the highest point, is the net force zero (i.e. are the forces balanced)? Explain how you
know.
The net force is not zero. The earth is pulling the ball down and there is no upward force
to balance it.
©Modeling Instruction 2013
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U4 Freeparticle, review v3.1
5.
You push a grocery cart along a level floor in the presence of friction
effects between the cart and the floor. Based on b and c, the cart is speeding up.
a. Draw force diagrams for you, the cart, and the floor/earth. Fully label
all vectors.
Fnet
Fnet
□□FN, c, f
□ FN, y, f
you
cart
=
**Ffs, y, f
*FN, y, c
=
* FN, c, y
○ Ff, c, f
=
=
◊ Fg, c, e
◊◊ Fg, y, e
b. While you are making the cart speed up, how does the size of the force you apply on the
cart compare to the size of the force the cart exerts on you? Explain.
These two forces are a 3rd Law pair so the forces must be equal.
c. While you are making the cart speed up, how does the size of the frictional force on the
cart by the floor compare to the frictional force on you by the floor?
The frictional force on you must be larger.
d. Identify all of the Newton’s Third Law pairs in your force diagrams.
The only one relevant here is that the force you apply to the cart must be equal and
opposite to the force the cart applies to you
©Modeling Instruction 2013
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U4 Freeparticle, review v3.1
6. A 35 kg child pulls a 12 kg wagon up a hill at 0.6 m/s. The wagon exerts 60 N of force on the child.
a. Draw a quantitative force diagram for the wagon.
FN = cos30°(12kg)10N/kg = 1.0x102 N
Fnet = 0
FT = 60N
║
30°
30°
Fg = 120 N
┴
b. Explain how you applied Newton’s first law to make the force diagram quantitative.
Since the object was moving at a constant velocity I knew that the tension force had to be
equal to the parallel component of the force of gravity. I also knew that the normal force
had to be equal to the perpendicular component of the force of gravity. The forces had to
add up to zero because the wagon was not accelerating.
c. Explain how you applied Newton’s third law to make the force diagram quantitative.
I knew that the force of the wagon on the child had to be equal to the tension force of the
child on the wagon. They are a 3rd Law pair.
7. a. Free body diagram with a spring force pointed up and a gravity force pointed down.
They are balanced.
b. Fs = Fg = 75*9.8 = 735 N
c. Fs = kx  k = Fs/x = 735 N/0.08 m = 9187.5 N/m
©Modeling Instruction 2013
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U4 Freeparticle, review v3.1