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Work
We are all familiar with the concept of work in both a physical
and scientific manner. For example, when one pushes or pulls
an object. It takes work! In fact, the more you pull or push (exert
a force) the greater the work and the farther you push or pull it
(greater displacement), the greater the work. So it is clear that
work depends on both the force and displacement. It is directly
proportional.
W α F
and
W α d
Work is done when a force is exerted on an object causing the
object to move in the direction of a component of the applied
force.
W = Fd
Where
F is the vector quantity force measured in Newtons (N)
d is the vector quantity displacement measured in metres (m)
W is the scalar quantity Work measured in Joules (J)
Work is a scalar quantity because it is the product of two
vectors.
One Joule is the amount of work done by a force of 1 N acting
through a displacement of 1 m.
An interesting point is that if there is no displacement, there is
no work even if a force is applied. So, pushing a concrete wall
may tire you out because you apply a large force, but no work is
done.
Example 1) How much work would be done by lifting a 50.0 kg
bag of flour 1.25 above the ground.
Positive and Negative Work
Work can be both positive or negative. However, work is a
scalar quantity so the negative/positive does NOT imply the
direction of the work, exactly.
Work is POSITIVE if the FORCE (or a component of force) is in
the SAME direction as the DISPLACEMENT.
Work is NEGATIVE if the FORCE (or a component of force) is
in the OPPOSITE direction as the DISPLACEMENT.
Work is ZERO if the FORCE (or a component of force) is
PERPENDICULAR to the DISPLACEMENT.
Example 2)
Peter is bench pressing a barbell that has a weight of 710 N.
What work is done when he raises the barbell a distance of 0.6
m above his chest? Is it positive or negative?
What work is done when he lowers the barbells? Is it positive or
negative?
Example 3) A person is pulling a mass to the right at a constant
speed with a force of 10 N for a distance of 2 m.
What is the work done by the person?
What is the work done by friction?
Free-body Diagrams and Work and Force at an Angle
You’ll recall from our work in projectile and circular motion; the
force component that is parallel to the motion will change the
magnitude of the velocity whereas the perpendicular component
will not affect the magnitude. The same is true for work.
Example 4) A 15 kg crate is being pulled to the right by a force
of 20 N over 25 m. The force is applied at an angle of 35° above
the horizontal. The kinetic friction is 5 N.
Draw a free-body diagram.
What is the work done by each force acting on the crate?
Total Work = ∑W OR
Total Work = FNETd
Example 5) A 20 kg crate is pushed 50 m along a horizontal
floor by a constant force of 100 N 23° below the horizontal and
the coefficient of kinetic friction is 0.25. Determine the total work
done.
What do you notice about the parallel component of the force in
each of the last two examples?
W = Fcosɵd
Work
We are all familiar with the concept of work in both a physical and scientific manner. For
example, when one pushes or pulls an object. It takes work! In fact, the more you pull or push
(exert a force) the greater the work and the farther you push or pull it (greater displacement), the
greater the work. So it is clear that work depends on both the force and displacement. It is
directly proportional.
W α F
and
W α d
Work is done when a force is exerted on an object causing the object to move in the direction of
a component of the applied force.
W = Fd
Where
F is the vector quantity force measured in Newtons (N)
d is the vector quantity displacement measured in metres (m)
W is the scalar quantity Work measured in Joules (J)
Work is a scalar quantity because it is the product of two vectors.
One Joule is the amount of work done by a force of 1 N acting through a displacement of 1 m.
An interesting point is that if there is no displacement, there is no work even if a force is applied.
So, pushing a concrete wall may tire you out because you apply a large force, but no work is
done.
Example 1) How much work would be done by lifting a 50.0 kg bag of flour 1.25 above the
ground.
Positive and Negative Work
Work can be both positive or negative. However, work is a scalar quantity so the
negative/positive does NOT imply the direction of the work, exactly.
Work is POSITIVE if the FORCE (or a component of force) is in the SAME direction as the
DISPLACEMENT.
Work is NEGATIVE if the FORCE (or a component of force) is in the OPPOSITE direction as
the DISPLACEMENT.
Work is ZERO if the FORCE (or a component of force) is PERPENDICULAR to the
DISPLACEMENT.
Example 2)
Peter is bench pressing a barbell that has a weight of 710 N. What work is done when he raises
the barbell a distance of 0.6 m above his chest? Is it positive or negative?
What work is done when he lowers the barbells? Is it positive or negative?
Example 3) A person is pulling a mass to the right at a constant speed with a force of 10 N for a
distance of 2 m.
What is the work done by the person?
What is the work done by friction?
Free-body Diagrams and Work and Force at an Angle
You’ll recall from our work in projectile and circular motion; the force component that is parallel
to the motion will change the magnitude of the velocity whereas the perpendicular component
will not affect the magnitude. The same is true for work.
Example 4) A 15 kg crate is being pulled to the right by a force of 20 N over 25 m. The force is
applied at an angle of 35° above the horizontal. The kinetic friction is 5 N.
Draw a free-body diagram.
What is the work done by each force acting on the crate?
Total Work = ∑W OR
Total Work = FNETd
Example 5) A 20 kg crate is pushed 50 m along a horizontal floor by a constant force of 100 N
23° below the horizontal and the coefficient of kinetic friction is 0.25. Determine the total work
done.
What do you notice about the parallel component of the force in each of the last two examples?
Learning Activity 4.1 – Work
1. A crate is being moved with a constant velocity by an applied force Fa that is parallel to
the direction of motion. The normal force, kinetic friction, and force of gravity also act on
the crate. Which forces are positive, negative, and zero?
2. The truck exerts a force of 2150 N to pull a car 16.2 m.
a. How much work is done by the truck?
b. How much work is done by the force of friction?
3. A person pulls horizontally with a force of 375 N against a crate of mass 125 kg and
moves it across the floor with a constant velocity of 1m/s for 3 seconds. How much work
is done?
4. Craig exerts a force of 150 N on a large crate for 2.5 seconds, but cannot move it. How
much work has been done?
5. A girls pulls a wagon with constant velocity along a level path for a distance of 45 m. The
handle of the wagon makes an angle of 20° with the horizontal, and she exerts a force of
85 N on the handle.
a. What work is done by the girl on the handle?
b. What work is done by friction?
6. You are moving into an apartment. Your weight is 685 N and that of your belongings is
925 N.
a. How much work does the elevator do in lifting you and your belongings up five
stories (15 m) at constant velocity?
b. How much work does the elevator do on you (without your belongings) on the
downward trip also at a constant velocity?
7. A 30 kg crate is pushed 40 m along a horizontal floor by a constant force of 90 N 27°
below the horizontal and the coefficient of kinetic friction is 0.27. Determine the total work
done.
8. A 100 kg crate is being pulled across a horizontal floor by a force of 203 N that makes an
angle of 30° above the horizontal. The crate moves at a constant velocity over a distance
of 2.5 m
a. Calculate the work done by the applied force.
b. Calculate the normal force acting on the crate.
c. Calculate the work done by the normal force.
d. Determine the coefficient of kinetic friction.