Download FBD practice solutions - knotts

Problem 1 solution: Which of the following are possible according to Newton's first and
third Laws? Explain your responses by providing an example for those that are possible,
and for situations not possible, state which laws are violated.
a. A body moves at constant velocity under the action of a single force.
Not possible. A single force on an object cannot result in balanced forces and a net force
of zero on an object. With a net force present, the object cannot have a constant velocity
according to Newton's first law.
b. A body experiences a force, but does not exert forces on any other bodies.
Not possible. "You can't touch without being touched." The object exerting a force on the
body experiencing the force feels an identical size force pushing back on it. Newton's
third law.
c. Two forces act on a body, and the body travels at a constant speed in a straight line.
Absolutely. When you rode the hovercraft, the two forces on you (gravitational and
normal) resulted in a net force of zero. When the net force is zero on an object, it travels
at constant speed in a straight line as described by Newton's first law.
d. A body accelerates without exerting forces on any other bodies.
Not possible. In order to accelerate, an unbalanced outside force is required as stated in
Newton's first law. The only way a runner, for example, can make the forces on her
unbalanced is by pushing back along the ground. The ground then pushes the runner
forward with an equal force as described by Newton's third law. If the ground is icy, the
runner's foot slips and is unable to exert a force backwards along the ground. Therefore
the ground cannot exert a force forward on the runner and she cannot accelerate.
e. A body exerts two forces on another object.
Absolutely. The earth, for example, can exert an upward normal force on you as well as a
downward gravitational force on you. A road exerts an upward normal force on your car
as well as a forward frictional force on your car. (Think carefully about the explanation
of the skater in part d if you aren't clear on the forward frictional force.)
f. A body moves at constant velocity without exerting forces on any other object.
Not really. Constant velocity without exerting forces on other objects is not possible
anywhere near the earth since we always are interacting with the earth through gravity.
Even deep in outer space, a gravitational interaction occurs since gravitational attraction
is a force that can act over infinite distances. As Newton's third law states, you
gravitationally pull just as hard on every star and planet in the universe as every star and
planet in the universe pulls on you.
g. A school bus drives along a straight road at constant speed under the action of a net
force.
Not possible. A net force will not result in constant speed according to Newton's first law.
Problem 2 solution: Compare the magnitudes of the following pairs of forces. Are the
forces a Newton's third law pair? Explain your responses.
a. The gravitational force the earth exerts on the moon, and the force on the earth by the
moon.
The forces are of equal magnitudes. This is a third law pair since it is the interaction
between the earth and moon.
b. The gravitational force on a book by the earth and the normal force on a book by a
bookshelf.
The forces are of equal magnitudes if the bookshelf is horizontal, but this is NOT a third
law pair because both forces are both on the book. The third law pair to the first force is
the gravitational force on the earth by the book, and the third law pair to the second force
is the normal force on the bookshelf by the book.
c. The force on a golf ball by a golf club, and the force on the club by the ball.
The forces are of equal magnitudes. This is a third law pair since it is the interaction
between the club and the ball. The ball hits the club just as hard as the club hits the ball.
d. The normal force on a skidding car by the road, and the frictional force on the car by
the road.
These are not a third law pair because both forces are on the car. They are not equal in
magnitude either, since the frictional force is always smaller than the normal force. The
third law pair to the first force is the normal force on the road by the car, and the third
law pair to the second force is the frictional force on the road by the car.
e. The force on a target by an arrow, and the force on the arrow by the target.
The forces are of equal magnitudes. This is a third law pair since it is the interaction
between the arrow and the target.
f. The force on a ball as you kick it by your foot, and the force on your foot by the ball.
The forces are of equal magnitudes. This is a third law pair since it is the interaction
between the ball and your foot.
g. The gravitational force on a rock on a hillside, and the normal force on the rock by the
hillside.
These are not a third law pair because both forces are on the rock. They are not equal in
magnitude either, since the normal force is equal to the component of gravity
perpendicular to the hillside. The perpendicuar component of gravity is smaller the
gravitational force on the rock. The third law pair to the first force is the upward
gravitational force on the earth by the rock, and the third law pair to the second force is
the normal force on the hillside by the rock.
Problem 3 solution: A 200 gram calculator rests on a 1.2 kg textbook which sits on a
table.
a. What is the weight of the textbook?
weight = 10 N/kg (mass) = 10 N/kg (1.2 kg) = 12 N
b. What is the weight of the calculator?
weight = 10 N/kg (mass) = 10 N/kg (0.2 kg) = 2 N
c. Draw force diagrams for the calculator and textbook.
d. Write an equation (without any numbers in it) for the vertical forces on the textbook.
FN,b,t = FN,b,c + Fg,b,e
e. Find the normal force on the book by the table.
FN,b,t = FN,b,c + Fg,b,e = 2 N + 12 N = 14 N
Problem 4 solution: A small car is pushing a stalled truck up a hill at constant speed.
a. Draw a force diagram for each vehicle.(The directions of the friction forces are tricky,
be careful.)
b. Identify any Newton's third law force pairs.
The only Newton's third law pair is the interaction between the car and the truck. FN,c,t
and FN,t,c.
c. Write an equation for the forces on the truck parallel to the hill.
FN,t,c = Ffr, t,h + Fg parallel truck
d. Write an equation for the forces on the truck perpendicular to the hill.
FN,t,h = Fg perp. truck
e. Write an equation for the forces on the car parallel to the hill.
Ffr, c,h = FN,c,t + Fg parallel car
f. Write an equation for the forces on the car perpendicular to the hill.
FN,c,h = Fg perp. car
g. Traveling up the hill at constant speed, how does the force of the car on the truck
compare to the force of the truck on the car?
FN,c,t and FN,t,c are equal. The truck pushes on the car just as hard as the car pushes on
the truck.
h. If the car is accelerating while pushing the truck up the hill, how does the force of the
car on the truck compare to the force of the truck on the car?
FN,c,t and FN,t,c are equal. The truck pushes on the car just as hard as the car pushes on
the truck. Yes, really! In the interaction between two objects, you can only touch as hard
as you are touched. If the car exerts more force on the truck to accelerate it up the hill, the
truck exerts more force back on the car.
i. Where does the net force come from that could allow the car to accelerate the truck up
the hill?
The net force does not come from the interaction between the car and the truck.
The net force arises from the frictional interaction between the car and the hill which is
larger than the frictional interaction between the truck and the hill. Friction with the hill
pushes the car up the hill harder than the hill resists the motion of the truck rolling up the
hill. The hill pushes the car UP the hill as the result of the Newton's third law interaction
from the car's tires pushing DOWN along the hill.