PHYS1006 Lecture Notes - Lecture 4: Net Force, Gravitational Energy, Elastic Energy
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Lecture 4: Work and Energy
Work
When a force moves an object through a certain distance we say work is completed.
Work done by a constant force
W = Fd
W = F cos d
W = Fd cos
Where F cos is the component of the force parallel to the displacement (d).
SI unit of work is joule (J)
1J = 1 N.m
Example 1
How much work did the movers do pushing a 160kg crate 10.3m across a rough floor
without acceleration, if k = 0.50 (friction)?
Fx = F – f
Fx = ma
F – f = 0 F = kmg
W = F d cos
W = (0.50 160 9.8) 10.3m cos0o.
W = 0.0081J
W = 8.110 3
J
Example 2
What is the minimum work needed to push a 950kg car 810m up a 9.0o incline when friction
is ignored?
Minimum work occurs when the car is moved with constant velocity.
Fy = N – mg cos
Fx = 0
Fx = F – mg sin
Fx = 0
W = F d
= mg sin d
= (950 9.8 sin9.0o) 810m
= 1200000J
= 1.2 10 6
J
Example 3
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What is the minimum work needed to push a 950kg car 810m up a 9.0o incline when friction
is included, k = 0.25 (friction)?
Fx = F – mg sin - k mg cos = 0
F = mg sin + k mg cos
Now we need to find the work
W = F d
W = (mg sin + k mg cos) d
It helps to rearrange the equation:
W = mg(sin + k cos) d
Mass = 950, g= 9.8, k = 0.25, = 9.0o and d = 810
W = 950 9.8(sin9.0o + 0.25 cos9.0o) 810
W = 3041752.081J
W = 3.0 10 6
J
The reason the work is more than in part (a) is because some of the work is done to
overcome the friction.
Energy
What is energy?
The ability to do work.
What is kinetic energy?
The energy of an object by virtue of its motion.
Kinetic energy = ½ Mass Velocity2
KE = ½ MV2
What is potential energy?
The energy of an object by virtue of its position or configuration.
Gravitational potential energy = mass gravity height
GPE = mgh
Elastic potential energy = ½ K x2
Work – Energy Principle
A net force (Fnet = ma) accelerates an object from initial velocity (Vi) to final velocity (Vf) over
a displacement (d). Therefore, the net work done on an object is equal to change in its kietic
energy.
Wnet = Fnet d
Wnet = Kf – Ki
Wnet = K
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Document Summary
When a force moves an object through a certain distance we say work is completed. Where f cos is the component of the force parallel to the displacement (d). W = (0. 50 160 9. 8) 10. 3m cos0o. Minimum work occurs when the car is moved with constant velocity. = (950 9. 8 sin9. 0o) 810m. Fx = f mg sin - k mg cos = 0. F = mg sin + k mg cos . W = (mg sin + k mg cos ) d. W = mg(sin + k cos ) d. Mass = 950, g= 9. 8, k = 0. 25, = 9. 0o and d = 810. W = 950 9. 8(sin9. 0o + 0. 25 cos9. 0o) 810. The reason the work is more than in part (a) is because some of the work is done to overcome the friction. The energy of an object by virtue of its motion. The energy of an object by virtue of its position or configuration.