Download Newton`s Second Law

Lyzinski Physics
CRHS-South
Newton’s Second Law
Let’s Review. Newton’s 1st Law says “An object in motion (or at rest) will stay in motion (or
at rest) unless acted upon by an unbalanced, external force”. Included in this statement is the
fact that objects naturally like to be either at rest or moving at a constant velocity. Their inertia
keeps them in one of these two natural motion states, and it requires an unbalanced, external force
to knock them out of their preferred motion state. Many forces can act on an object at rest, but
unless the forces are unbalanced, the object will not move. The same can be said for objects
moving at a constant velocity.
Now for the one million dollar question. What happens to an object if an unbalanced, external
force DOES act upon it? The answer is simple: its motion will change. In other words, it will
accelerate. Newton’s 2nd Law explains what will happen to this object. Stated in the simplest
terms, it says
FNET = ma
Implied by this law are two proportions, namely
and
In other words, if you double the net force acting on an object, the acceleration will double. If you
quarter the net applied force, the acceleration will be quartered. Also, if you double the mass of an
object, the applied force needed to accelerate it (at a certain rate) must also be doubled. If the mass
of an object is tripled, the applied force must also be tripled in order to accelerate it at the same
rate.
Newton’s 2nd law has a vector nature. This is REALLY important. It can be broken down into
both the x-direction and the y-direction as follows:
FX = maX
and
FY = maY
This is pretty simple to understand. The net force in the x-direction will accelerate the object in the
x-direction. Therefore, to find the acceleration in the x-direction, you divided the force (in the xdirection) by the mass. The same rule applies for the y-direction. Therefore, when using Newton’s
2nd Law, you always need to look at the direction that the object is accelerating, and only deal with
the forces in that particular direction. If the object is not moving in a certain direction, can you still
use Newton’s 2nd Law? Of course. However, you use FNET = ma = m(0) = 0.
When dealing with objects and the forces acting on them, it is important to look at ALL the forces.
These forces include
* Friction
* Pushes
* Weight
* Air resistance (a form of friction)
* Pulls (which included “tensions” – coming soon)
* Normal Forces (huh?)
Force due to gravity: A field force (a vector quantity) that always is directed towards
the center of the earth.
Weight: The magnitude of the Force due to gravity.
Fg = W = mg
gearth = 9.8 m/s2
gmoon = 1.6 m/s2
Mass: A measure of an objects inertia
Weight: Decreases as you move away from the
(its tendency to resist a change in
center of the earth. NOT an inherent
its motion). Inherent property of
property of an object
an object.
Examples:
a) Find the earth weight of an object whose mass is 60 kg.
b) If an object weighs 700N on the moon, what is its mass on the moon? What is its
mass on the earth?
Free-Body Diagrams
Block falling
through the
air
Block
resting on
the ground
Pulling a box
along the
ground
Pushing a
block along
the ground
In-class examples
1) An 50 kg object is accelerating at a rate of 5 m/s2 to the right. Find the net force acting on
the object.
2) Three forces (50N [S], 60N [W], and 30N [E] ) act simultaneously upon a 30 kg object.
Find the object’s acceleration.
3) A man pushes a 60 lb lawnmower across the grass with a constant horizontal force of 30N.
If the lawnmower moves with a constant velocity, find the force of friction opposing the
lawnmower’s motion.
4) A box is accelerated from rest along a frictionless surface by a net force of 100N. It covers
40 meters in 5 seconds. Find the mass of the box.
5) A father (80 kg) pulls his son (30 kg) in a radio-flyer wagon (10 kg). The handle of the
wagon makes an angle of 40o with the horizontal, and the dad pulls with a force of 200N.
First, draw an FBD (free-body-diagram) of this situation, showing all the forces acting on
the wagon. Then, find the acceleration of the wagon if …
a) the ground is frictionless (which, by the way, is highly unlikely)
b) the ground provides a constant frictional force of 30N.
6) A 30 kg box is pushed along a frictionless surface. The person pushing the box pushes with
a constant force of 300 Newtons directed at an angle of 30o below the horizontal. If the box
starts from rest and reaches a speed of 5 m/s after only 2 seconds of pushing, find the force
of friction acting on the box. Make sure to start with a complete FBD of the box, showing
all the forces acting upon it.
7) A skydiver of mass 75 kg is falling through the non-physics-land air. Eventually he reaches
a terminal velocity and falls at a constant speed. Find the resistive force (from the air) that
acts on the skydiver at this time. Make sure to start with a complete FBD, showing all the
forces acting upon the skydiver.
8) Explain the relationship between Newton’s 1st Law and his 2nd Law.
Book HW: Buffa pp. 132-134 #'s 14-15, 18, 21
Newton’s Second Law Worksheet (part 1)
1. A 5 kg box is sitting at rest on a perfectly frictionless surface. Suddenly, a 100 N forces
pulls it eastward. Find the acceleration of the box.
2. A 300 kg block is sitting at rest on a perfectly frictionless surface. Two 25N forces act on
the block, one directed east and one directed west. Find the acceleration of the block.
3. A block of unknown mass sits on a perfectly frictionless surface. It is pulled by a force of
100 N [S] and pushed by a force of 50 N [N]. The magnitude of its acceleration is 9 m/s2.
Find the mass of the block as well as the direction of the acceleration.
4. An object is pulled in two opposite directions along a frictionless surface by forces of 50
kN [E] and 30 kN [W]. If the object is accelerated at 5 m/s2, find the object’s mass.
5. A 40 kg box is pulled from rest at an angle of 30o above the horizontal with a constant
force of 500N. If the force of friction opposing the motion is 100N, find the box’s
acceleration. How far will it move in 7 seconds? What will its velocity be after these 7
seconds?
6. A 100 kg block is sitting on a perfectly frictionless surface. A force of 200 N directed at an
angle of 30o above the horizontal pulls the block. Find the acceleration of the block.
7. A block is pulled along a surface at a constant velocity by a force of 200 N. Find the force
of friction opposing the movement.
8. A 60 kg block is being pulled along a surface by a force of 100N. If the magnitude of the
block’s acceleration is 1.2 m/s2, find the force of friction opposing the movement. Start off by
drawing a full Free-Body-Diagram (FBD) of the block.
9. A 1.0 kg toy car is moving across a smooth floor with a velocity of 5.0 m/s. An unbalanced
force of 2.0 N acts on the car for 4.0 s. Determine the velocity of the car at the end of the
interval in each of the following cases:
(a) if the force acts in the direction of motion of the car.
(b) if the force acts in the opposite direction to the motion of the car.
Hint: First, for each case, find the acceleration of the car. Then, use an equation of
motion.
Buffa HW: Buffa pp. 132-135 #'s 28, 29, 66, 67
Newton’s Second Law Worksheet (part 2)
10. An electron has a mass of 9.1 x 10–31 kg. Between the electrodes of a cathode-ray tube, it
moves a distance of 4.0 mm, accelerated by a net electrical force of 5.6 x 10–15 N.
Assuming that it started from rest, find its acceleration and its final velocity.
11. A bullet of mass 20 g strikes a fixed block of wood at a speed of 320 m/s. The bullet
embeds itself in the block of wood, penetrating to a dept of 6.0 cm. Calculate the average
net force acting on the bullet while it is being brought to rest.
12. A 2 kg block is pulled across a frictionless surface by forces of 5N [E], 16 N [SW], and 10
N [S 30 E]. Find the magnitude and direction of the block’s acceleration. (Can you say
tug-o-war? J)
13. A 9 kg ball falls through the air, which resists the ball with a constant force of 9N. Draw a
free-body diagram of the ball and then find its acceleration. Why is the acceleration of the
ball NOT equal to g? Fully explain.
14. If an object is moving at a constant velocity, explain what Newton’s 2nd law says about the
object. Does this agree with or disagree with Newton’s 1st Law.
15. A 3-car train is being pulled on frictionless tracks. The lead car is has a mass of 2000 kg,
while the 2nd two cars each have masses of 1500 kg. How much force is required to
accelerate the train at 3 m/s2? If the train is being pulled by this force and the last car
suddenly detaches, what will its new acceleration be?
10 N
16. Two girls pull a sled from rest across a field of snow, as shown
in the diagram. A third girl pulls backward with a 2.0 N force.
All forces are constant. If the mass of the sled is 10 kg,
determine its instantaneous acceleration. Then, determine the
time required for the sled to move a distance of 10 m.
2N
30°
10 kg
40°
10 N
(A view from above, or a “bird’s eye view”, is assumed in this problem)
17. The graph shows the velocity of a 5.0 kg radio-controlled toy car, moving in a straight line,
as a function of time. Plot a force-time graph for the car.
v (m/s)
5.0
4.0
3.0
2.0
1.0
0
t(s)
2
4
6
8
10
12
14