FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s 2 .
-Refer to Figure 8-5. What is the speed of the bead at point C?

Question

FIGURE 8-5  A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s 2 .
-Refer to Figure 8-5. What is the speed of the bead at point C?

Quizplus · Accepted Answer

Since there is no friction, the energy of the bead is conserved. At point A, the bead has potential energy mg(2R) where R is the radius of the loop. At point C, the bead has kinetic energy 1/2mv^2 and potential energy mgR. Setting these equal to each other we get: mg(2R) = 1/2mv^2 + mgR. Cancelling out the mass, we get: g(2R) = 1/2v^2 + gR. Solving for v, we get v = sqrt(2gR) which equals 2 m/s with R = 0.5 m. Therefore, the speed of the bead at point C is 2.0 m/s.

FIGURE 8-5 a 2