Solving a Pendulum Physics Problem: Finding the Height of a Colliding System

[Clutch306]

Two pendulums, both of length l = 1.0m, are initially situated as shown in the below figure. The left bob has a mas m1 = 1.0kg and is held a distance d = 0.50m above the center of the right bob, of mass m2 = 2.0kg. The left pendulum is released and strikes the other. Assume that the collsion is completely inelastic, and neglect the mass of the string and frictional effects. How high does the pendulum system rise after the collision?

 

[arildno]

1. Use conservation of mechanical energy on the swinging pendulum to determine its impact velocity.
2. Use impact analysis to determine the system's velocity after impact.
3. Use conservation of energy of the system to determine the max. displacement.

 

[M98Ranger]

To solve this pendulum physics problem, we can use the conservation of energy principle. Initially, the left pendulum has gravitational potential energy equal to m1*g*d, where g is the acceleration due to gravity and d is the distance the bob is held above the center of the right bob. This potential energy is converted into kinetic energy as the left pendulum swings down and collides with the right pendulum.

Since the collision is completely inelastic, the two pendulums will stick together after the collision and move as one system. The kinetic energy of the system just before the collision is equal to the sum of the kinetic energies of the two individual pendulums. This can be calculated using the formula 1/2*m*v^2, where m is the mass and v is the velocity of each pendulum.

After the collision, the combined pendulum system will rise to a certain height h, where all the energy is now in the form of gravitational potential energy. Using the same formula as before, m*g*h, we can equate the initial potential energy to the final potential energy and solve for h.

m1*g*d = (m1+m2)*g*h

Substituting in the given values, we get:

1.0kg*9.8m/s^2*0.50m = (1.0kg+2.0kg)*9.8m/s^2*h

4.9 = 3*9.8*h

h = 4.9/29.4 = 0.167m

Therefore, the combined pendulum system will rise to a height of 0.167m after the collision. This is the final answer to the problem.