4 Newton’s Laws: Explaining Motion
Answers to Questions
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Galileo was active in the late 16th and early 17th centuries while Newton worked during the late 17th and
early 18th centuries. Aristotle preceded them both by about two thousand years. (For a different view
contemporary with Aristotle, search for information regarding the lesser-known philosopher Aristarchus.)
Aristotle believed that a larger object was subject to a larger force and that velocity was proportional to
force. Therefore the velocity of a larger object falling to the ground had to be greater than the velocity of a
smaller mass falling to the ground. He believed that this was validated by the fact that holding the objects
in one’s hand one could compare forces.
According to Aristotle the thrown ball moves and displaces air that rushes backwards to fill the vacuum left
by the ball in the vacated position. This air serves to push the ball forward.
He assumed that there was a constant force being applied by the air rushing by the object to fill the
“vacuum” left behind. No, this does not seem reasonable.
No, but his relationship between distance and constant acceleration is a subset of Newton’s more complete
laws.
The larger mass has a smaller acceleration. For a given force, the ratio of the accelerations will be the
inverse of the ratio of the masses.
No. It is equal. According to the second law, force is mass times acceleration. Half the mass times twice
the acceleration yields the same force.
No. The forces add to zero, so the first law applies.
The object may be moving--it just won't be accelerating.
No. Without any other force to change its motion, the bullet will continue moving undisturbed until and
unless something does interact with it.
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21
Q22
Q23
Yes. There will be a net force.
Yes. There must be a net force directed opposite the motion to produce the observed negative
acceleration.
a. No. The velocity of the car is continuously changing direction while on the curve so there is
acceleration.
b. Yes. A net force is required to produce acceleration.
Yes. However, the first law does not give the mathematical relationship between forces, acceleration and
mass.
No. Mass is an intrinsic property of matter, while weight is a force resulting from an object under the
influence of Earth’s gravitational field.
Yes. They both accelerate at the same rate. The forces are different because their masses are different.
Mass is intrinsic to the body; it won’t change by the move. The rock’s weight will change because
acceleration due to the moon’s gravitational field is weaker than Earth’s.
Mass is not a force. As stated above it is a property of matter arising from the structure of matter. Weight,
however, is a force. Weight is mass times acceleration (due to gravity).
a. Since the can of lead contains more mass than the can of feathers, the can with lead shot will
experience a greater force of gravity.
b. Both experience the same acceleration due to gravity. The can with the lead experiences the greater
gravitational force but its mass is greater in exactly the same ratio.
The normal force and the gravitational force are both acting on the boy. The force of gravity acts
downward. The floor exerts an equal upward force. Since these forces act upon the same body they cannot
constitute an action-reaction pair. The fact that they are equal is a consequence of Newton’s first law.
The force of friction between pavement and the drive wheels propels the car forward. This is a reaction to
the force of the wheels pushing back on the pavement, due to friction.
With little or no friction, there will be little or no force to change the motion of the car.
a. There are two forces acting on the ball; tension from the string and force due to gravitation.
b. The net force equals zero. The ball is not accelerating in any direction.
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Q24
Q25
Q26
Q27
Q28
c. The reactions are the ball’s force on the string and the ball’s gravitational force on the Earth.
Yes, but the change in momentum is small because the time during which the force is applied is small.
a. The runner pushes his/her feet backward against the starting blocks. The reaction of the starting
blocks on the runner is the force initially accelerating the runner.
b. At the desired maximum velocity the runner would only have to exert enough force to overcome air
resistance.
Yes. The mule can accelerate the cart assuming said mule is strong enough to impart a horizontal
component of force that will overcome the horizontal frictional force necessary to get the cart wheels
moving.
No. The forces in Newton’s 3rd Law act on different objects.
Normal force
toy tractor
reaction
force of
book
friction
weight
Normal force
friction
book
pushing of tractor
weight
Q29
Q30
Q31
Q32
Q33
Yes. The acceleration of the two masses will be equal and will cause m 2 to fall and m1 to rise.
a. They will not move with constant velocity but with constantly increasing velocity. The applied force is
constant, and this implies a constant acceleration. Constant acceleration results in constantly
increasing velocity.
b. The tension in the connecting string is less than F. Both bodies have the same acceleration. The force
F accelerates a total mass, 2m. The force in the connecting string accelerates a mass, m, so it is half of
F.
In the absence of a velocity independent resistive force, the skydiver will experience a constant force and a
resulting constant acceleration. There will be no terminal velocity.
The normal force will be less than your true weight because the normal force will now equal your true
weight plus the descending force.
No. The gravitational force is accelerating both the elevator and me downward at 9.8 m/s 2. The normal
force does, however, equal zero.
Answers to Exercises
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
E13
E14
8 m/s2
15 N
5 kg
25 m/s2
1.5 m/s2
a. 18 N
b. 2 N
5 kg
a. 20 N
b. 5 m/s2 to the right
a. -2.5 N
b. -0.625 m/s2
392 N
20 kg
a. 490 N
b. 50 kg
a. 61.2 kg
b. 135 lb
The second man of 735 N has the greater mass.
2
E15
E16
E17
E18
E19
6.05 m/s2 downward
14 N upward
a. 4.9 N
b. 10.9 N, no.
a. 3.3 N
b. 2.2 m/s2
a. +72 N
b. -588 N
c. +660 N
Answers to Synthesis Problems
SP1
SP2
SP3
SP4
SP5
SP6
SP7
a.
b.
c.
a.
b.
c.
d.
a.
b.
c.
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
e.
a.
b.
c.
d.
5.0 m/s2
15 m/s
22.5 m
1.0 m/s2
60 N
190 N
190 N; Net force would have to equal zero.
0.375 m/s2
.075 m/s
0.75 cm
Yes. The crate will accelerate toward the floor (down) because the net force is directed downward.
1.67 m/s2 downward
1.29 s
2.16 m/s
16 N
2.67 m/s2
11.33 N
10.67 N on block a = 2.67 m/s2; same as b.
600 N
84 N downward
516 N
516 N
84 N upward; 672 N; 672 N
350 N
4.57 m/s2
75 m/s
If the cause is brief, the increase in velocity will be countered by the increase in frictional force of air
resistance, which will cause windburn and a dissipation of heat as the skydiver is slowed back down to
terminal velocity.
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