Download Chapter 5: The Laws of Motion Tori Cook PROBLEMS NEWTON`S

Chapter 5: The Laws of Motion
This unit uses Newton's Laws to explain what mechanism
causes acceleration, and why certain objects accelerate more
than others. It deals mostly with the concept of force.
NEWTON’S LAWS
Newton's First Law: In the absence of external forces, an object at
rest remains at rest and an object in motion continues in motion
with a constant velocity.
Newton's Second Law:
Newton's Third Law: If two objects interact, the force exerted by
object 1 by object 2 is equal in magnitude and opposite in direction
to the force exerted by object 2 on object 1.
More Things to Remember
1.
For a freely falling object, the acceleration a equals g, the
gravitational constant of 9.8 m/s
2.
The two forces in an action-reaction pair are always
acting on different objects; two forces acting on the same object
do not make up an action-reaction pair
3.
A free-body diagram is an invaluable tool for depicting
all the forces acting on one object
Tori Cook
Key Terms
equilibrium: the state of an object
that is moving at a constant
velocity (includes objects at rest)
net force: the sum of all the forces
acting on an object
newton: the unit of force, 1N=1
kg*m/s
normal force: the force applied
perpendicular to a surface by that
surface on an object resting on top
of it
tension: the force exerted by a
rope on an object hanging from it,
opposing gravity
friction: the resistance to the
motion of an object, results from
the object interacting with its
surroundings
coefficient of friction: the
constant that dictates how much
friction will result when two
objects interact—remember that
the coefficient of static friction
(when both objects are still) is
higher than the coefficient of
PROBLEMS
kinetic friction (when the objects
are moving in relation to one
1. [Easy] A block of mass m rests on a frictionless incline at an angleanother)
θ from the horizontal.
What is its acceleration?
2. [Medium] A hockey puck with a mass of .30 kg slides on the frictionless surface of an ice
rink. Two hockey sticks strike the puck simultaneously, exerting the two forces shown below.
The force F1 has a magnitude of 5.0 N and the force F2 has a magnitude of 8.0N. Determine
the magnitude and direction of the puck's acceleration.
y
Chapter 5: The Laws of Motion
Tori Cook
x
3. [Hard] A block of mass
on a rough, horizontal surface, is attached to a ball of mass
by a lightweight cord that passes over a frictionless pulley of negligible mass. A force of
magnitude F is applied at an angle θ to the block. The coefficient of kinetic friction between
the block and the surface is . Determine the magnitude of the acceleration of the two
objects.
F
a
θ
a
Solutions
1. Draw a free-body diagram. The only forces acting on the
block are the normal force and gravity. Write out the general
force equation.
Chapter 5: The Laws of Motion
Tori Cook
Write out an equation for each force acting on the block.
*Note that we put in the term sin θ when calculating the normal force because we are only
interested in the component of the normal that acts parallel to gravity.
Rewrite the general force equation to include the forces that we just calculated. Remember
that the normal force and gravitational forces are acting in opposite directions. I have
designated downward as being the positive direction.
2. For this problem, we will want to calculate the components of the net force exerted on the
puck in the x and y directions.
We can find the x components using cos and the y components using sin. Remember that the
angles are relative to the x-axis, and so the angle below the axis should be negative.
We can now use Newton’s Second Law to calculate the components of acceleration.
Chapter 5: The Laws of Motion
Tori Cook
To find the resultant of these two vectors, we just have to use the Pythagorean Theorem.
To find its direction relative to the x-axis, we need to use a trigonometric identity.
3. First we must draw free body diagrams for each of the objects.
Then, we have to write force equations for
each object. Be sure to include all the forces.
T
F
T
f
*The x component of the acceleration of the
block is going to equal the y component of
the acceleration of the ball, since the two are
connected.
Solve for T using the second equation.
We also need to remember that the force of friction is reduced because of the y component of
F, which is pulling the block off the horizontal surface.
Put this back in the original equation and solve for acceleration!