Download 3 3 Newton`s Second Law

When an unbalanced force acts on an object, the object will
accelerate in the same direction as the force. The
acceleration varies directly as the force, and inversely as the
mass.
To really appreciate Newton’s Laws, it sometimes helps to see
how they build on each other.
The first law describes what will happen if there is no force,
and the second law describes what will happen if there is a
force.
Let’s break the law down to what it really means . . . .
“When an unbalanced force acts on an object . . . .”
The forces acting on the object do NOT balance.
The terms net force and unbalanced force mean the same thing.
F net  zero
“ ... the object will accelerate in the same direction as the force . . .”
Do NOT confuse this to mean that the object will move in the same direction as
the force. This is not necessarily true.
If you understand
and remember this,
you’re set!!
A net force causes an object to accelerate.
If an object is accelerating, then the forces acting on it are not balanced.
If an object is moving at a constant velocity, it is NOT accelerating and therefore
the net force acting on it is zero. The forces acting on it are balanced.
“ . . . The acceleration varies directly as the force . . .” a  F net
They depend directly on each other.
α
is the
Greek letter
alpha and
means
“varies as” in
For example, if you push twice as hard, the object’s
acceleration doubles.
“ . . . and inversely as the
mass.”
They depend inversely on each other.
1
a
m
math
If you apply a force to a bigger mass, it will be harder to accelerate.
When you put the two
together, you get:
F net
a
m
F net  ma
F net
m
a
= net force (N)
= mass (kg)
= acceleration (m/s2)
The S.I. unit for force is the newton.
1 newton = 1 N
It is a vector quantity, so you need to include direction.
The newton is an example of a derived
unit.
A derived unit can be written in terms of other fundamental units.
Examples of fundamental units are:
metres (m), seconds (s), kilograms (kg)
From the formula for net force, we look at the units:
F net  ma
(N)
so . . . .
1 N = 1 kg m/s2
(m/s2)
(kg)
“One newton equals one kilogram metre per second squared.”
We will apply Newton’s Second Law
to Various Types of Questions:
I.
II.
III.
IV.
V.
Horizontal Motion
Vertical Motion
Two body systems
attached by a string
or rope on a
horizontal surface.
Single Pulley
Systems in the
Vertical Plane
Two Pulley Systems
on a horizontal
surface.
I. Applying Newton’s Second law to Horizontal
Motion
Hint:
1. Determine the accelerations which result
when a 12-N net force is applied to a 3-kg
object and then to a 6-kg object.
Always
draw a FBD
first!!!!!! And
always write your
F net statement!
2. A net force of 15 N is exerted on an encyclopedia to cause it to
accelerate at a rate of 5 m/s2. Determine the mass of the
encyclopedia.
3. Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is
tripled and the mass is doubled, then what is the new acceleration of the sled?
4. A 4.0 kg object is accelerated uniformly from rest to a velocity of 30 m/s west in
8.5 s. What is the net force acting on the object during this acceleration?
14 N west
5. A net force of 30.0 N north acts on a 17.5 kg object. If this object accelerates
uniformly from a velocity of 2.00 m/s north to a velocity of 9.00 m/s north, what
was the displacement of object while accelerating?
22.5 m north
6. Bob is pushing a 40 kg box east using a force of 65 N, the box starts at rest and
moves east 5.0 m in 8.0 s, assume uniform acceleration.
a.
draw a free body diagram
b.
find the acceleration of the box (kinematics)
c.
what is the force due to friction?
7. Net Force Causes Acceleration Lance Armstrong uses a force of 80 N to ride his bike
west, the wind exerts a force of 60 N east, Lance and his bike have a mass of 75 kg.
a.
Draw a FBD
b.
What is the net force on Lance?
8. A 20 kg box slides east across the floor with an initial velocity of 3.2
m/s, the box comes to a complete stop in a distance of 4.0 m.
HINT: Friction is the only force there is no other applied force
because the box is already moving.
a. Draw a FBD, show all forces
b. What is the force of friction on the box?
II. Applying Newton’s Second law to Vertical Motion
1.
2.
3.
4.
Draw an FBD!
Remember acceleration due to gravity is 9.81 m/s²
Chose what direction you will call positive and negative.
Start by writing an Fnet statement!
1. A person on an elevator have a combined
mass of 600 kg. The elevator cable exerts a
force of 6.50 x 10 ³ N [up] on the elevator.
a. Find the acceleration of the person.
b. What do we call the force that is due to the
elevator cable?
2. A 55 kg female bungee jumper fastens one end of the cord (made of an elastic
material) to her ankle and the other end to a bridge. Then she jumps off the
bridge. As the cord is stretching, it exerts and elastic force directed up on her.
a. Write the F net statement and FBD for the jumper.
b. Calculate her acceleration at the instant the cord exerts an elastic force of 825 N
[up] on her.
3. A toy rocket has a mass of 1.20 kg and the motor exerts a
force of 15.0 N. The rocket motor fires for 6.00 s.
a.
b.
c.
d.
e.
draw a free body diagram
what is the net force on the rocket?
what is the height of the rocket after 6.00 s?
what is the velocity of the rocket after 6.00 s?
what maximum height does the rocket reach?
4. A ball has a mass of 0.240 kg and is thrown straight up
into the air, the initial acceleration of the ball is 2.69 m/s2.
What is the applied force on the ball?