| Contents for this page | Related topics |  |
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Work Work performed against gravity Work done accelerating an object from rest Additional questions |
Projectiles Conservation of momentum in two dimensions Energy Power |
 Data
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| Learning Outcomes | ||
| After studying this section, you will understand and be able to apply the concepts of work. | ||
| Helpful background knowledge | ||
| Introduction to vectors | Addition of vectors | Equations of motion |
If an object is moved through a distance, s, by the action of a net force, F, acting in the direction of the motion, then WORK has been done on the object by the force.
The amount of work done in moving an object is the product of the component of the force acting on the object parallel to the displacement, F, and the magnitude of the displacement, s, i.e.
Work is a SCALAR QUANTITY, which is normally given the symbols W or w. The unit of work is the JOULE, (J), which is the amount of work done on an object when a force of 1 newton produces a displacement of 1 metre.
If a force F acts along a rope which is attached to an object, as shown on the right, |
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and produces a horizontal displacement s, |
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it is only the component of the force in the direction of the displacement which does the work. |
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Thus, w = Fcosθ s. When θ = 90°, cosθ = 0, so, work is not done in a direction perpendicular to the point of application of a force.
Similar considerations apply to an object which is moving in a circle, such as a weight attached to a string and whirled in a circular motion. The force maintaining the object in its orbit is always perpendicular to the displacement of the object and thus no work is done by this force. Note also that if an object moves at a constant velocity over a frictionless surface, no force acts on the object and thus no work is done in order to produce the displacement. |
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Similarly, if a force is used to maintain equilibrium and in doing so produces no displacement of the object, then no work is done by the force.
 | The force required to lift an object of mass, m, near the surface of the earth is mg, that is, the weight of the object, directed upwards. When it is raised to a height, h, the object is displaced by a distance h in the direction of the force. |
Thus the work done against gravity, wg, in raising an object of mass m through a height h is given by
If a force, F, is applied to a stationary object of mass, m, on a frictionless surface, the object accelerates from rest. After the object has moved a distance, s, the work done by the force will be w = Fs |
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From Newton's second law (
), the force, F, is related to the acceleration, a, by
F = ma
and from the equations of motion, the velocity, v, of the object after it has moved a distance, s, is given by
v2 = 2as
The acceleration is thus a = v2/2s
Thus, the work required to cause an object of mass, m, to be accelerated from rest to a velocity, v, is given by
This is the kinetic energy of the body. Equally, the work that needs to be done in order to stop a body of mass, m, travelling at a velocity, v, is given by w = ½mv2.
Glossary