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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
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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?
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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)
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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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