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m23 work problems (1)

# m23 work problems (1) - First recall the definition of...

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First recall the definition of force from Newton’s Law that Force = mass x acceleration In symbols, F = ma Work is a technical term meaning the product of force F and the displacement caused by it. In symbols, W = F d
When stalled car is pushed, the speed that the car attains depends on the force F with which it is pushed and the distance d over which that force is applied . Thus, force and distance are the ingredients of work W = F d

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If you push against an immovable object, such as a brick wall, you may tire yourself out, but you will perform no work. Why?
Common units for measuring force Newtons (N) in the International System of Units (SI) one newton is the force required to give a mass of 1 kg an acceleration of 1 m/s 2 Dynes (dyn) in the CGS system one dyne is the force required to give a mass of 1 g an acceleration of 1 cm/s 2 Pounds (lb) in the British Engineering system one pound of force is the force required to give a mass of 1 slug an acceleration of 1 ft/s 2

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The total work done in moving an object along an axis, say the x -axis from point a to b , if the force exerted at point x obeys the law F = F ( x ) , is Example Suppose an object is moved along the x -axis from x = 1 cm to x = 5 cm, and suppose that the force obeys the law F = F ( x ) = x 2 + x dynes. Find the total work done. (Eq.2)
A particle is moving along the x -axis from a to b according to the force law F ( x ) which is given. Find the work done. 1. F(x) = x 3 + 2x 2 6x + 4 from x = 0 to x = 2 2. F(x) = 2x 2 + 3x + 5 from x = -1 to x = 3 3. F(x) = x 3 + x from x = -1 to x = 2 4. F(x) = (x 2 + 2x + 1) 3 (x + 1) from x =0 to x = 2 5. F(x) = x(1 + x 2 ) 1/2 from x = 1 to x = 2

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Hooke’s Law states that within the limits of elasticity the displacement produced in a body is proportional to the force applied.

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