Download Problem Set 4 – Newton`s Laws and Forces

Problem Set 3 – Newton’s Laws and Forces
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Due Wednesday March 28
All your work is to be done on separate sheets of paper.
Each of your responses must be numbered the same way as it appears on the
question sheet.
Show your work
Pen or pencil is acceptable. Please no red pens, we’ll use those to score in class.
1) Define these terms
a. Inertia
b. Contact force
c. Long range force
d. Mass
e. Weight
f. System and environment
(surroundings)
g.
h.
i.
j.
k.
l.
Static equilibrium
Dynamic equilibrium
Vector
Normal Force
Static Friction
Kinetic Friction
2) Why are both of these statements FALSE – explain your thoughts…
a. If an object is at rest, there can be no forces acting upon the object.
b. A force can exist by itself
3) If a perfectly round pool ball is rolling on a perfectly smooth, frictionless surface,
will it keep rolling at a constant speed, or will it eventually slow to a stop?
Explain your answer.
4) A 2 kg picture is hung by two wires of equal length
that make an angle of 30º with the horizontal as
shown in the diagram to the right. Find the tension in
each wire.
30º
60º
30º
T
T
2 kg
20 N
5) A 10 kg object is subjected to two forces F1 and F2, as shown in the diagram to
the right. A third force F3 is applied so that the object is in static equilibrium. Find
F3. (remember forces are vectors)
10 kg
30º
30 N
6) A block of mass 15 kg is hanging from three cords
(A, B, C). What are the tensions in each of the cords.
Look at the diagram to the right.
47º
60º
28º
A
B
C
15 kg
7) If Jade is coasting along a flat icy road on a sled, and she turns, but maintains the
same speed, is there a net force acing on her? If so, what is supplying the net
force?
8) Lucy has just won the gold medal in ski jumping (thanks to her work on projectile
motion)! As they hang the gold medal around her neck she is impressed with its
mass (576 g) and she wonders what is weight is… help her figure it out!
9) If Oliver took that 576 gram medal to the moon on his next trip what would
change about the gold Lucy earned, its mass, its weight, neither, or both?
Explain.
10) While on the moon from the previous question, Oliver notices that the
acceleration due to gravity is about 1/6th that on earth. How much would Lucy’s
576 g of gold weigh on the moon? SHOW YOUR WORK.
11) If on Oliver’s voyage back to earth, he takes a wrong turn and end up floating
about in outer space nowhere near a planet, what is the mass of Lucy’s gold
medal? What is its weight?
12) Marie is pulling her kid brother along in a sled. If she increases the force on his
already moving mass, what happens to the sled’s acceleration? EXPLAIN.
13) If Seppe tosses a dozen rotten eggs off the top of the Empire State Building, will
they keep accelerating all the way to ground? Why or why not?
14) A 50.0 N gymnast is hanging onto a bar that is supported by two ropes. What is
the tension in each rope?
15) If Dan knocks on a door with a force of 50.0N, what does the door do to Dan?
16) Tim is a 90.0 kg winger on the hockey team and he pushes against the boards in a
hockey rink with a force of 35.0 N and recoils. What acceleration does Tim
experience?
17) Devan is 100.0 kg and is skating at the rink, he pushed against the boards with
enough force to recoil at an acceleration of 0.40 m/s2. What force did Devan
apply to the boards?
18) Mr. Williamson is skating at the rink, too. He pushes off the boards with a force
of 66.0 N. He accelerates to 1.32 m/s2. What is Mr. Williamson’s mass?
19) Newton’s Third Law tells us that for every action there is an equal and opposite
reaction. Identify the action and reaction forces for a flashlight falling out of
Nate’s hand and bounces off the ground. If a force is exerted on the earth as the
flashlight falls, why doesn’t the earth move? Explain.
20) A 630 kg bobsleigh is initially at rest in the middle of a flat, long, deserted, icy
road. Dill has to apply a 75 N horizontal force to set it in motion. What is the
coefficient of static friction between the bobsleigh and the icy road?
21) A 20.0 kg curling stone given a 100.0 N push by Cam. The coefficient of friction
between the stone and the ice it is traveling along is 0.12. Does the stone move?
If so, what is its acceleration?
22) If someone had recently remade the ice surface (zambonied it) and the coefficient
of friction was decreased to 0.04, what force would Cam have to apply to move
the 20.0 kg stone?
23) The rising concern among athletic trainers and health advocates (and parents)
regarding concussions and multiple concussions among high school student
athletes has prompted numerous studies of the effectiveness of protective head
gear and the forces and accelerations experienced by players. One study suggested
that there is a 50% chance of concussions for impacts rated at 75 g's of
acceleration (i.e., 75 multiplied by 9.8 m/s/s). (The average head impact results in
22 to 24 g's of acceleration.) If a player's head mass (with helmet) is 6.0 kg and
considered to be a free body, then what net force would be required to produce an
acceleration of 75 g's (~740 m/s/s)?
24) Anna Litical and Noah Formula are experimenting with the effect of mass and net
force upon the acceleration of a lab cart. They determine that a net force of F
causes a cart with a mass of M to accelerate at 35 cm/s2. What is the acceleration
value of a cart with …
a. a mass of M when acted upon by a net force of 2F?
b. a mass of 2M when acted upon by a net force of F?
c. a mass of 2M when acted upon by a net force of 2F?
d. a mass of 4M when acted upon by a net force of 2F?
e. a mass of 2M when acted upon by a net force of 4F?
25) Skydiving tunnels have become popular attractions, appealing in part to those
who would like a taste of the skydiving experience but are too overwhelmed by
the fear of jumping out of a plane at several thousand feet. Skydiving tunnels are
vertical wind tunnels through which air is blown at high speeds, allowing visitors
to experience body flight. On Mr. Walsh's first adventure inside the tunnel, he
changes his orientation and for an instant, his 78.8-kg body momentarily
experiences an upward force of air resistance of 521 N. Determine Mr. Walsh’s
acceleration during this moment in time.
26) While skydiving, Dee Selerate opens her parachute and her 55.5-kg body
immediately accelerates upward for an instant at 8.66 m/s2. Determine the upward
force experienced by Dee during this instant.
27) Tim is playing catch. He exerts a forward force on the 0.146-kg baseball to bring
it to rest from a speed of 33.2 m/s. During the process, his hand recoils a distance
of 0.134 m. Determine the acceleration of the ball and the force which is applied
to it by Tim as he catches it.
28) Lucy, Cam, Cherokee and Seppe are playing hockey at CREW. As Cam and Lucy
chase after the 0.162 kg puck, it decelerates from 12.5 m/s to 8.4 m/s in 11
seconds.
a. Determine the acceleration of the puck.
b. Determine the force of friction experienced by the puck.
c. Determine the coefficient of friction between the ice and the puck.
29) Dan is driving his 1570-kg car. It is skidding to a stop along a horizontal surface.
The car decelerates from 24.6 m/s to a rest position in 3.05 seconds. Assuming
negligible air resistance, determine the coefficient of friction between the car tires
and the road surface.
8.0 k g
4 kg
30) In the diagram above the coefficient of friction between the block and the table is
0.25. Assuming the pulley is frictionless; determine the acceleration of the
system.
31) A 4.0 kg mass and a 3.0 kg mass are suspended from either end of an atwood’s
machine. What is the acceleration of the system?
32) Draw free-body diagrams for an Olympic athlete…
a. Standing still on the podium listening to their national anthem
b. Coasting horizontally across a finish line at a constant velocity after
skating.
c. Sprinting horizontally across a finish line at an increasing velocity
d. Sliding to a stop in his backside after being checked at center ice.
e. Sliding down a bobsleigh track at a constant velocity.
f. Accelerating down a the same track
33) What are the net forces of the following on an Olympian if:
a. Two fans pull on opposite arms with a force 20 N right, 30 N left.
b. A team mate lifts up on his waist with 4.0 N as his mom hugs him to the
right with 50N of force.
c. Two fans pull on opposite arms with a force 20 N right, 30 N left, a team
mate lifts up on his waist with 23.0 N as his dad tries to tackle him to the
ground with 32 N of force.
34) Cases I through IV in the table below represent four states of motion for a curling
stone on a horizontal icy surface. First, using the stones below the table, draw the
free-body diagrams showing the forces acting on the pumpkin in each case. Using
the quantities given in the table, fill in the blanks in the table. Show all of your
equations, substituted values, and answers with correct units on a separate sheet.
Quantity
velocity (v)
mass (m)
weight (W)
normal force (N)
force of friction (Ff)
coeff. of friction ()
applied force (FA)
net force (Fnet)
acceleration (a)
Case I
0
2 kg
Case II
constant
Case III
changing
35 N, down
60 N, down
60 N, up
24 N, left
0
N/A
5 N, down
0.2
Case IV
changing
9 kg
0.3
18 N, right
.333 m/s2, right
Coordinate system
+ (up)
+(right)
Case I
Case II
Case III
Case IV
The Elevator Problem
A 70-kg man stands on a scale that measures weight while riding in an elevator.
Calculate what the scale will read in each of the following situations:
I. The elevator is at rest.
II. The elevator is moving up with a constant velocity.
III. The elevator is moving down with a constant velocity.
IV. The elevator is accelerating upward at 3 m/s2.
V. The elevator is accelerating downward at 4 m/s2.
Background Information
 The scale does not always read the true weight of the man. It only reads the force exerted on it by the
man's feet. His true weight is the force exerted on him by the gravitational pull of the earth, whereas
the scale reads his apparent weight.
Let's see how we can use Newton's laws of motion to find the apparent weight of the man under the
circumstances listed above.
 The only forces on the man are:
1. The force pulling down on him due to gravity (his true weight, W)
2. The force pushing up on the bottom of his feet by the scale, FM.
Applying Newton's 2nd law we can write: F = FM + W = ma
 Now, since the forces FM and W act in 1-D (along the same line) we can signify the direction of any
vector quantity in the problem by letting all vectors up be positive and all those down be negative.
Rewriting the equation above considering directions yields: F = FM - W = ma (Equation A)

Newton's 3rd law tells us that the force exerted on the man's feet is equal in magnitude but opposite
in direction to the force that his feet exert on the scale. As stated above, the scale reading
(his apparent weight) is the force exerted on the scale. Or, in fewer words:
Apparent weight = scale reading = Fs
We are now ready to analyze situations I-IV mathematically in order to determine the man's
"apparent" weight in each situation.
I. When the elevator is at rest, a = _____ because F = FM - W = _____.
Therefore, FM = W = _______ and the scale will read ________.
II and III. When the elevator is moving up or down at constant velocity, a = _____
and F = FM - W = _______. Therefore the scale will read _______.
IV. When the elevator is accelerating upward at 3 m/s2, F = FM - W gives the force necessary to
give him this acceleration. Thus, in equation A we must substitute W = _______ , m = ______ and
a = _______. Therefore, the push up of the scale on his feet = _______. This force is equal in
magnitude but opposite in direction to the force his feet exert on the scale. The scale reads this force
during the acceleration as _________.
V. Using the same method as in IV, we can calculate the scale reading when the elevator in
accelerating downward at 4 m/s2. In this situation the man’s apparent weight is ________.
Extension: What would be the apparent weight of the man if the cable supporting the elevator
snapped when the elevator was stopped at the 10th floor? How fast would the elevator be going when
it hits the basement 35 m below the 10th floor?