A small ball with a mass of 4.1 kg moves along with the energy curve shown to th

Question

A small ball with a mass of 4.1 kg moves along with the energy curve shown to the left, while not being subjected to any non-conservative forces. At point B it has a velocity of 2.7 m/sec.

1. What is the mechanical energy of the object at point B? MB =

2. What is the mechanical energy of the object at point A?MEA=

3. What is the mechanical energy of the object at point D? MED=

4. What is the net work done by conservative forces on the object between points B and C? WconB-C=

5. What is the velocity of the object at point C?vC=

Explanation / Answer

Given,

m = 4.1 kg ; v = 2.7 m/s ;

No non conservative forces acting on the ball.

1)At point B, its ME will be:

ME = PE + KE = 2 + 1/2 x 4.1 x 2.7 x 2.7 = 16.9 = 17 J

ME(B) = 16.9 = 17 J(Aprox)

2)ME(A) = 17 J ; Since No non conservative forces are acting, the value of ME has to be same at the given points. The increase/decrease in PE or KE will be compensated by one another.

3)ME(D) = 17 J, same explanation as 2.

4)Work done by the conservative forces = change in mechanical energy. But it did not change, So the net work done is zero.

5) ME = PE + KE

17 = 5 + 0.5 x 4.1 x Vc2

Vc = 2.42 m/s

Hence, velocity at point C is Vc = 2.42 m/s

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