Pushing shopping cart with a variable force

Pushing shopping cart with a variable force - Pushing...

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Pushing shopping cart with a variable force Consider the same example as above, but this time, let our force change with position. Suppose that in the beginning it takes a little while (3m) for our force to get up to its maximum value, and then we get tired and push weaker over the final 3m. Now we’d like to calculate the velocity of the cart by the 10m mark. as before. Now to calculate the work done by our force, we must calculate the area under the F-x curve. This area is: and so the final velocity will be: Example: Shoving box up an inclined plane w/ friction (work done by g, f k ) Suppose we shove a 40kg box up an inclined plane at a velocity of 5m/s. If μ k = 0.25, and the angle of inclination is 20 deg, to what height will the block go before coming to rest? We will apply the work-energy equation. Let Δr be the distance the block travels up the incline. Take a minute to observe again that the work done by normal force is 0 since it is perpendicular to the motion of the block. Now from N2L, So we have, and also recognize that h = Δrsinθ, and so Δr = h/sinθ. So,
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