Two simple pendulums of equal length l = 0.45 m are suspended from the same point. The pendulum bobs are small solid steel spheres. The first bob is drawn back to make a 35° angle with the vertical, while the other one is left hanging at rest. If the first bob has a mass of 0.25 kg and the second has a mass of $0.54 \mathrm {~kg} \text {, }$ how high will the second bob rise above its initial position when struck elastically by the first bob after it is released?
A) 3.3 cm
B) 2.7 cm
C) 3.9 cm
D) 4.4 cm

Question

Quizplus · Accepted Answer

Explanation:The total mechanical energy of the system is conserved. The initial energy is all potential energy stored in the first bob, and the final energy is all potential energy stored in the second bob. Therefore, we have:$$m_1gy_1 = m_2gy_2$$where $m_1$ and $y_1$ are the mass and height of the first bob, and $m_2$ and $y_2$ are the mass and height of the second bob. Solving for $y_2$, we get:$$y_2 = \frac{m_1y_1}{m_2} = \frac{(0.25 \mathrm{~kg})(0.45 \mathrm{~m})}{0.54 \mathrm{~kg}} = 0.21 \mathrm{~m} = 21 \mathrm{~cm}$$Therefore, the second bob will rise 21 cm above its initial position.

Two Simple Pendulums of Equal Length L = 0 0.54 kg, 0.54 \mathrm {~kg} \text {, }0.54 kg,

Two Simple Pendulums of Equal Length L = 0 $0.54 \mathrm {~kg} \text {, }$