AUTOMATIC 5 STARS FOR CLEAR AND CONCISE ANSWER WITH F.B.D (IF NECESSARY) Delta U

Question

AUTOMATIC 5 STARS FOR CLEAR AND CONCISE ANSWER WITH F.B.D (IF NECESSARY)

Delta U = -W U(y) = mgy U(x) = 1/2 kx2 F(x) = dU(x)/dx There is a block of mass m on a frictionless plane that is tilted at an angle Theta relative to the horizontal. While being pulled np the slope by an applied force that is parallel to the slope, it accelerates with acceleration a over a distance d. a) Show that the amount of work done by the applied force over distance d is given by Wa = mad. Show that the amount of work done by gravity over distance d is given by Wg = -mgd sin Theta.

Explanation / Answer

a) work done = force * displacement = ma* d = mad

b) since the vertical component of d is d*sin(@)

so y= d sin(@)

U(y)= mgd sin(@)

W= -U = -mgd sin(@)

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