1) A bead slides without friction on a curved wire as shown in the figure above.

Question

1) A bead slides without friction on a curved wire as shown in the figure above. If the height of point A relative to B is 0.45 m, then what is the speed of the bead when it reaches point B? Assume that the bead is at rest at point A.

2)Starting from rest, a ball of mass 3 kg is accelerated at 7 m/s2 for 7 s. What is the final kinetic energy (in J) of the ball after 7 s?

3)Starting from rest, a ball of mass 4 kg experiences a constant force of 24 N for 8 s. What is the final kinetic energy (in J) of the ball after 8 s?

Explanation / Answer

1. Applying energy conservation,

PE+ KE at A = PE +KE at B

m g h + 0 = 0 + m v^2 /2

v = sqrt(2 g h) = sqrt(2 x 9.8 x 0.45) = 2.97 m/s

2. v = u + a t = 0 + (7 x 7) = 49 m/s

KE = m v^2 /2 = 3 x 49^2 /2 = 3601.5 J

3. Impulse = change in momentum

24 x 8 = 4 ( v - 0)

v = 48 m/s

KE = 4 x 48^2 /2 = 4608 J

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