First slide

Work done by Diff type of forces

Question

A 1 kg mass is projected down a rough circular track (radius = 2.0 m) placed in vertical plane as shown. The speed of the mass at point A is 3 m/s
and at point B, it is 6.0 m/s. How much work is done on the mass between A and B by the force of friction?

Moderate

A

-7.5 J
B

-8.5 J
C

-6.5 J
D

-24 J

Solution

Conservation of energy principle
KE at A = $\frac{1}{2} \times 1.0 \times 3 . 0^{2} = 4.5 J$
Loss in PE between A and B =1.0 x l0 x 2 = 20J
Gain in KE from A to B if there had been no friction = 20J
Total KE at B if there had been no friction
= 4.5 + 20 = 24.5 I
But actual KE at B = $\frac{1}{2} \times 1.0 \times 6^{2}$ = 18 J
Loss in energy due to friction = 24.5 - l8 = 6.5 J

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