Download Benchmark 1 Study Questions SOLUTIONS

Information
Newton’s First Law
Newton's first law of motion is often stated as an
object at rest tends to stay at rest and an object in
motion tends to stay in motion with the same speed
and in the same direction unless acted upon by an
unbalanced force.
In fact, it is the natural tendency of objects to resist
changes in their state of motion. This tendency is
described as inertia. A more massive object has a
greater tendency to resist
changes in its state of
motion.
Forces are Balanced
Objects at Rest
Objects in Motion
V = 0m/s
V ≠ 0m/s
a = 0 m/s2
a = 0 m/s2
Stays at Rest
Stays in Motion
V = 0m/s
Same Velocity
Inertia: the resistance an object has to a change in its state of motion.
Forces are said to be balanced when the net force on the object are zero.
That is when all the forces are added up the result is zero. For example
when you are standing the force of gravity is balanced by the force of the
floor holding you up.
Forces are unbalanced when the net force is not zero. In a tug-of-war both
teams apply forces. For a team to win the forces must be unequal or
unbalanced. You want the net force to be in your direction.
Critical Thinking Questions – Part II
1. Restate Newton’s first law in terms of acceleration.
An object will continue in its state of motion unless an unbalanced
force is acting on it.
2. If the forces are balanced what is the resulting acceleration?
If forces are balanced, then the net force equals 0. This means that there is
no acceleration.
3. An object’s resistance to change in motion is dependent solely on what quantity?
An object’s resistance to change in motion is only dependent on its MASS.
4. Inertia is the resistance to change in motion so inertia depends solely on what?
MASS
5. What is required to cause acceleration?
An unbalanced force (or non-zero net force) is
needed to cause acceleration.
6. What is the net force if you push a cart to the right with 5N of
force and a friend pushes the cart to the left with 5N of force?
In this case, the forces are balanced so the net force
is 0.
7. What is the net force if you start to pull instead of pushing in
#6?
The net force would be 10 N to the left in this case.
Exercises
1. Imagine a place in the cosmos far from all gravitational and frictional influences. Suppose
that you visit that place (just suppose) and throw a rock. What will the rock do? Why?
The rock will continue to move at a constant speed because there will be no unbalanced
forces acting on the rock (no gravitational or frictional forces).
2. Supposing you were in space in a weightless environment, would it require a force to set an
object in motion? Explain.
Yes, Newton’s 1st law still applies. Since an object will have the same mass in the
weightless environment as it does on Earth, a force is required to set it in motion.
3. Why doesn’t a ball roll on forever after being kicked at a soccer game?
The ball doesn’t roll forever because there is an unbalanced force acting on the ball
causing it to slow down. The main force causing the ball to slow down and stop is
FRICTION.
4. A 2-kg object is moving horizontally with a speed of 4 m/s. How much net force is required
to keep the object moving at this speed and in this direction? Explain.
The object will continue moving at 4 m/s unless an unbalanced force acts on it.
So, no force (0 N) is needed for the object to keep moving at the same speed
and in the same direction.
5. Ben Tooclose is being chased through the woods by a bull moose which he was attempting to
photograph. The enormous mass of the bull moose is extremely intimidating. Yet, if Ben
makes a zigzag pattern through the woods, he will be able to use the large mass of the moose
to his own advantage. Explain this in terms of inertia and Newton's first law of motion.
A large mass means that there is a greater resistance to changes in motion compared to
a small mass. It is easier for Ben to change his motion during a zigzag pattern than it will
be for the moose to change its motion because Ben has a smaller mass in comparison to
the moose.
6. Luke Autbeloe drops an approximately 5.0 kg object (weight = 50.0 N) off the roof of his
house into the swimming pool below. Upon encountering the pool, the object encounters a
50.0 N upward resistance force (assumed to be constant). Use this description to answer the
following questions. (Down is usually considered a negative direction)
a. Which one of the velocity-time graphs best describes the motion of the object? Why?
When the object is dropped from the roof, it starts off with a negative velocity which will become MORE negative and faster
as time goes on. Once the object hits the water, the forces are balanced and it will continue to move at a constant velocity.
b. True or False: Once the object hits the water, the forces are balanced and the object will
stop. Support your answer with reasoning.
FALSE. When the forces are balanced, the object will not change its motion from that point forward.
This does not mean that the object will stop moving but rather that it will continue to move at the
velocity that it was moving at when it hit the water.
Information
Newton’s Second Law
As stated in the first law, the presence of an unbalanced
force will accelerate an object - changing either its speed,
its direction, or both its speed and direction.
Newton's second law of motion pertains to the behavior
of objects for which all existing forces are not balanced.
The second law states that the acceleration of an object is
dependent upon two variables - the net force acting upon
the object and the mass of the object. The acceleration is
always in the same direction as the net force.
Forces are Unbalanced
a≠0
Depends directly
on the net force
Depends inversely
on object’s mass
Mathematically this means:
acceleration =
Forcenet
;
mass
commonly written as:
a=
Fnet
m
Fnet = ma
Do not use the value of merely any force in the above equation. It is the net force which is
related to acceleration. The net force is the sum of all the forces acting on an object.
Critical Thinking Questions – Part III
1. What two variables is acceleration dependent on? What is the relationship between these
variables and acceleration? (i.e. if you increase one variable what happens to the
acceleration?)
Acceleration is dependent on the net force and the mass of the object. Acceleration is DIRECTLY related
to force (if force increases, acceleration must also increase, and vice versa). Acceleration is INVERSELY
related to mass (if mass increases, acceleration must decrease).
2. If an object is not accelerating what can you determine about the sum of all the forces on the
object?
If an object is not accelerating, that means that the net force on the object (sum of all the forces
on the object) is 0.
3. If the net force on an object is in a negative direction, what will the direction of the resulting
acceleration be?
The acceleration will also be negative if the net force on the object is in the negative direction.
4. If you double the net force on an object what is the result on the acceleration?
F = m x a. If the net force is doubled, the acceleration is also doubled. (Force and acceleration are
DIRECTLY related.)
5. If you double the mass of an object while leaving the net force unchanged what is the result
on the acceleration?
F = m x a. If the net force is unchanged and the mass is doubled, the acceleration must be halved (half of
what is was before)
F = (2m) x (1/2 a) Remember that mass and acceleration are INVERSELY related.
6. A Cadillac Escalade has a mass of 2 569.6 kg, if it accelerates at 4.65m/s2 what is the net
force on the car?
F = m x a = (2569.6 kg) x (4.65 m/s^2) = 11,948.64 N
7. A 7.26kg bowling ball (16 pounds) is at rest at the end of a bowling lane. Use this
information to answer the following questions.
a. What is the net force acting on the ball?
When the bowling ball is at rest, the net force acting on the ball is 0 N.
b. You push the ball with a force of 22.8N which induces a -2.3N frictional force.
What is the net force while you push the ball?
There is a -2.3 N frictional force opposing the force that is applied to the ball.
The net force is 22.8 N - 2.3 N = 20.5 N since the forces are acting in opposite directions.
(Since there are no specific directions given in the problem, we can’t include a direction for net force.
c. What is the acceleration caused by your push on the ball?
F = m x a -> a = F/m = 20.5 N/7.26 kg = 2.8 m/s^2
d. Following your push the ball rolls down the lane at 4.2m/s. What is the net force
on the ball as it rolls down the lane at the constant speed?
The ball is rolling at a constant speed so there is no acceleration. Since there is no acceleration,
there is no net force (0 N) acting on the ball.
e. CHALLENGE: How long did you push the ball in this situation?
Exercises
8. Complete the following table. Be sure to include units in your answer.
Net Force (N)
Mass (kg)
Acceleration
5.0
2.5
2.0 m/s^2
2.32
12
0.19 m/s^2
18.2
1.967
9.25 m/s^2
0.87
21.2
0.04 m/s^2
180
1.793
100.39 m/s^2
9. Complete the following table. Be sure to include units.
Net Force (N)
16 N
25.0
53
172.44
4201.75 N
Mass (kg)
Acceleration (m/s2)
4.0
4.0
5.0 kg
3
4.998
17.67 m/s^2
36.96 kg
4.665
1 225
3.43