Download Newton`s 2d Law of Motion

Dynamics
Newton’s Second Law of Motion
Do Now
1. Write down the algebraic equation
representing the 2d Law of Motion.
2. What effect the change in one of the variables
in the equation will have on the acceleration?


Fnet
m
a
a. m=constant
Double the net force ->acceleration_____
Half the net force-> acceleration_______
b. Fnet = constant
Double the net force-> acceleration_____
Half the net force-> acceleration_______
Equilibrium
• Objects at equilibrium (the forces acting upon
the object are balanced, net force = 0) do not
accelerate.
Net Force Causes Acceleration
• If an object is not at rest and is not moving at a
constant velocity then there is a net force that
causes change in motion, or accelerated motion.
• Acceleration = Change in Velocity/ Time Interval
Acceleration and Net Force
• Acceleration depends on
net force.
• To increase the acceleration
of an object, you must
increase the net force on
the object.
• If you double the net force,
the acceleration doubles.
• Acceleration is directly
proportional to the net
force.
• Acceleration ∝Net Force
Mass Resists Acceleration
If you apply the same force to an empty and
loaded shopping cart, the loaded shopping cart
will accelerate slower.
Acceleration and Mass
• For the same force, the acceleration produced is
inversely proportional to the mass.
1
• acceleration ∝
mass
• If you apply force to twice as much mass the
acceleration is twice smaller.
• If you triple the mass, the acceleration is three
times smaller.
Newton’s Second Law of Motion
• The acceleration produced by a net force on
an object is directly proportional to the
magnitude of the net force, and inversely
proportional to the mass of the object.

Fnet
• acceleration ∝
mass

 Fnet
a
m


Fnet  ma
Direction of Acceleration
• Acceleration has the same direction as the net
force. (Think of pulling an imaginary rope to
change the motion of the object).
Practice Problems
1. Two forces, F1 =12 N and F2=2N, are applied to
a block on a frictionless horizontal surface. If the
magnitude of the block’s acceleration is 2.0
m/s/s, what is the mass of the block?
F1
F2
Do Now
A 25-newton northward force and a 35-newton
southward force act concurrently on a 15-kg
object on a frictionless surface. What is the
magnitude of the object’s acceleration.
3. A net force of 10 N accelerates an object at 5
m/s/s. What net force would be required to
accelerate the same object at 1.0 m/s/s?
Questions
• How does acceleration depend on the net force?
• How does acceleration depend on the mass of
the object?
• According to the Second Law of Motion, a =
F
m
• Does the direction of acceleration depend on the
net force?
Do Now
• Calculate the acceleration of a 100 kg cart
when the net force on it 50 N.
F
a
m
50 N
a
100kg
• a = 0.5 m/s/s
Free Fall Explained
• Consider the free-falling motion of a 1000-kg
baby elephant and a 1-kg overgrown mouse.
Acceleration of Gravity
• This ratio (Fnet/m) is sometimes called the
gravitational field strength and is expressed
as 9.8 N/kg (for a location upon Earth's
surface).
• Because the 9.8 N/kg gravitational field at
Earth's surface causes a 9.8 m/s/s acceleration
of any object placed there, we often call this
ratio the acceleration of gravity.
• Free-body diagrams for four situations are
shown below. For each situation, determine
the net force acting upon the object.
• Free-body diagrams for four situations are
shown below. The net force is known for each
situation. However, the magnitudes of a few
of the individual forces are not known.
Analyze each situation individually and
determine the magnitude of the unknown
forces.
2d Law of Motion.
Practice Problems
• 1. Determine the accelerations that result
when a 12-N net force is applied to a 3-kg
object and then to a 6-kg object.
• 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. Suppose that a sled is accelerating at a rate of
2 m/s2. If the net force is tripled and the mass is
halved, then what is the new acceleration of the
sled?
• 5. A force of F newtons causes mass m of m
kilograms to accelerate at 24 m/s2. What
acceleration will occur under the following
conditions:
a) The force is doubled to 2F newtons, and the
mass remains the same.
•
• b) The force is F newtons and the mass is tripled.
6. Calculate the acceleration of a 300 000-kg jumbo
jet just before takeoff when the thrust for each of
four engines is 30 000 N.
7. Calculate the horizontal force that must be applied
to a 1-kg puck to make it accelerate on a horizontal
friction-free with the same acceleration it would
have if it would be dropped and fell freely.
a=g=10 m/s/s
8. a. Calculate the acceleration it you push with
a 20-N horizontal force on a 2 kg block on a
horizontal friction-free air table.
b. What acceleration occurs if the friction force
is 4 N?
Newton’s Second Law of Motion – Force and
Acceleration
Review Questions.
6.1 Forces Cause Acceleration
1. When a hockey puck is struck with a hockey
stick, an unbalanced force acts on the puck and
the puck accelerates.
2. d. unbalanced
3. net force
4. increases
5. c. A net force on an object causes acceleration.
6. A net force acts on both carts. The net force on
the cart that accelerates faster, is 3 times greater
than the other force (masses of the cars are
equal).
6.2 Mass Resists Acceleration
• 7. If the force is constant, the increase in mass
will result in decrease in acceleration.
• 8. When one quantity increases, the other
quantity decreases.
• 9. b. acceleration ~ 1/mass
6.3 Newton’s Second Law.
• 10. a. mass
b. force
d. acceleration
• 11. a. acceleration is directly proportion to the net
force.
b. the direction of acceleration is the same as net
force.
c. the acceleration is inversely proportional to mass
• 12. m/s2 kg
• 13. True
• 14. d. 200 N
• 15. d. halving the mass
• 16. The object accelerates at the same rate.
• 17. a. a  F
m
6.6 Free Fall Explained.
• 32. free fall
• 33. They both strike the ground at the same time
if there is no air resistance.
• 34. gravity
• 35. a. They all fall with the same acceleration.
b. The net force acting on them is their weight.
c. Their weight to mass ratios are always the
same.
d. Their acceleration is g, the acceleration due to
gravity.