Download Brock University Physics 1P21/1P91 Fall 2013 Dr. D`Agostino

Brock University
Physics 1P21/1P91
Fall 2013
Dr. D’Agostino
Solutions for Tutorial 5: Chapter 4, Forces and Newton’s Laws of Motion
The goals of this tutorial are:
• understand the concept of force
• understand Newton’s laws of motion
Clearly indicate whether each statement is TRUE or FALSE. Then provide a clear, detailed
explanation for why the statement is true or false. If the statement is false, make sure to
include a correction.
1. When a car brakes suddenly, a passenger in the car is thrown forward by the force of
the car’s motion. [2 points]
Solution: FALSE
Remember that force is not something that an object can have; rather, an object exerts
a force on another object.
Saying that the car’s motion carries a force is wrong; objects don’t carry force along
with their motion. The phrase “the force of the car’s motion” makes no sense; the
car’s motion doesn’t have any force.
When the car brakes, there is NO force that pushes the passenger forward. The
passenger feels that he is thrown forward because of his own self-centred perspective.
However, if the car were invisible, an outside observer would see the passenger slowing
down and stopping, not being thrown forward.
To repeat, there are no forces pushing the passenger forward. Rather, it is the tendency
of a moving object to continue moving in a straight line at its current speed (i.e., the
object’s inertia) that is at work here. According to Newton’s first law, the passenger
would continue travelling forward at constant speed when the car brakes, unless some
forces act to change the passenger’s motion. Ideally, the seatbelt will safely slow the
passenger down to a stop when the car brakes; otherwise, the windshield or the road
will do the job.
If you think that something is pushing the passenger forward, ask yourself what is the
agent that exerts the force on the passenger in the forward direction as the car brakes.
Go through the list of common forces; you’ll see that there is no agent that exerts a
force on the passenger in the forward direction as the car brakes.
2. You are in the passenger seat of a car that drives to the left around a sharp curve at
high speed. You feel that you are thrown towards the right passenger door. The force
of the car’s motion is pushing you towards the door. [2 points]
Solution: FALSE. This is very similar to the previous question. There is no force
pushing the passenger towards the door; the passenger feels that this is so because of
his self-centred perspective. In fact, it is the passenger’s inertia at work; the passenger
has a tendency to continue in a straight line at a constant speed as the car turns. The
car door turns into the path of the passenger’s motion, and “gets in the way” of the
passenger’s tendency to move straight.
Nothing pushes the passenger towards the door. There is no agent that exerts a force
on the passenger in the direction of the door. On the contrary, it is the door that
exerts a force on the passenger in the direction of the centre of the circular arc of the
car’s curved path.
If the car door did not exert such a force on the passenger, and no other forces were
exerted on the passenger, then the passenger would continue travelling in a straight
line at a constant speed. For example, if the car were a jeep with no doors, and the
seats were very slippery, and there were no seat belts, then maybe the passenger would
exit the car while it was turning.
If you think that something is pushing the passenger “outwards” as the car drives
around the curve, ask yourself what is the agent that exerts the force on the passenger
in the outward direction as the car turns. Go through the list of common forces; you’ll
see that there is no agent that exerts a force on the passenger in the outward direction
as the car turns.
3. A ball is thrown straight up. At the peak of the motion, the ball stops momentarily.
Because the ball is stopped momentarily, it experiences no force for that instant. [2
points]
Solution: FALSE. There are two common misconceptions that may be at work here.
The first misconception is that if the velocity is zero then the acceleration must be
zero; this is false. Remember that the acceleration is the rate of change of velocity, so
there may be acceleration present no matter what the velocity is. In other words, even
if the velocity is momentarily zero, the velocity may be changing, which means that
the acceleration is not zero.
The second misconception is that if the velocity is zero then the net force acting on
the object must also be zero. This is also false; remember that the net force acting on
an object is directly related to its acceleration (via Newton’s second law of motion),
not the velocity. Thus, even if the velocity of an object is momentarily zero, the net
force acting on the object is not necessarily zero.
In our specific example, the acceleration of the ball is constant throughout its motion,
and we call it the acceleration due to gravity. Even at the peak of its motion, when
the velocity of the ball is momentarily zero, gravity still acts on the ball, and the ball
still has a downward acceleration.
Of course, if an object has zero velocity for an extended period of time (not just
momentarily), then its acceleration is zero, and the net force on it is also zero. Don’t
confuse this situation, where an object is “just sitting there” for a long time, with the
ball thrown vertically upwards, which has zero velocity just momentarily.
4. A ball is twirled in a circle at a constant speed. Because the speed is constant, the ball
experiences no net force. [2 points]
Solution: FALSE: A ball moving in a circle accelerates in every moment. Draw a
circle and plot some of the velocity vectors at each point of the motion (as you did in
a previous tutorial). Notice that the direction of the velocity vector changes in every
moment, even if the magnitude does not. So, even if the speed is constant (so that the
magnitude of the velocity does not change), the direction of the velocity does change,
and so the velocity changes. This means that there is acceleration, and so by Newton’s
second law there must be a net force that causes the acceleration.
Where does the force come from in this case? The string (or whatever is attached to
the ball) pulls on the ball; this is the force that causes the acceleration.
Don’t confuse constant speed with constant velocity; constant speed does not necessarily mean constant velocity, as this example shows.
5. You sit in a chair. Gravity acts downward on you. The chair exerts no force on you,
it merely gets in the way and prevents you from falling to the floor. [2 points]
Solution: FALSE. This is another common misconception. Some people think that
only animate objects or mechanical devices (people, animals, maybe robots or machines) can exert forces. Inanimate objects, such as chairs, floors, walls, etc., can also
exert forces.
The net force on you is zero, because you sit in the chair without moving. But there is
a downward gravitational force on you, exerted by the Earth. The only way that the
net force on you can be zero (which must be so, according to Newton’s second law of
motion), is that there must be an upward force on you that balances the gravitational
force on you. The upward force acting on you is exerted on you by the chair.
6. You are in a canoe, and use your paddle to push off the dock to get your canoe moving.
The dock exerts an equal and opposite force on you, so the net force on you is zero
while your paddle touches the dock. [2 points]
Solution: FALSE. It’s common to make mistakes about which forces act on which
objects; it’s wise to be careful about this, and always ask yourself about which objects
are exerting a force, and which objects they are exerting a force on. In applying
Newton’s second law of motion, we usually focus attention on a single object and ask
ourselves about all the forces exerted on it by other objects. This can be challenging,
as we’re more used to attending to the forces that an object exerts, not the forces being
exerted on an object.
The specific mistake made in the given statement is that the two forces described act
on different objects. It’s true that the force that you exert on the dock (using your
paddle) is equal in magnitude and opposite in direction to the force that the dock
exerts on you (in accord with Newton’s third law of motion). However, one of these
forces acts on you, and the other acts on the dock, and so it makes no sense to add
them.
If it were true that the net force on you were zero, then you would not be able to push
yourself away from the dock with your paddle. (If the net force on you were zero, so
would the acceleration, by Newton’s second law of motion.)
Only add forces that act on the same object, to determine the net force acting on the
object.