Question

As part of a carnival game, a mb = 0.653kg ball is thrown at a stack of 21.3cm tall, mo = 0.343kg objects and hits with a perfectly horizontal velocity vb,i = 11.1m/s.Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of vb,f = 4.35m/s in the same direction, the topmost object has an angular velocity of wo = 4.83rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of torque due to gravity during the collision is negligible. what is the center of mass velocity vo,cm of the tall object immediately after it is struck?

Answer 1

The center of mass velocity (vo,cm) of the object immediately after being struck by a ball in a carnival game can be calculated using the conservation of linear momentum. The momentum before the collision is the incoming ball's momentum, and after the collision, it is the sum of the momenta of the ball and the object. With given values for mass and velocities, we can find vo,cm mathematically.

Step-by-step explanation:

The question asks for the center of mass velocity (vo,cm) of the tall object immediately after it is struck by a ball. To solve this, we can apply the principle of conservation of linear momentum, which states that the total momentum of a closed system before and after a collision remains constant if no external forces are acting on the system.

Before the collision, the linear momentum is given by the mass of the ball times its initial velocity. After the collision, the momentum is shared between the ball, now moving slower, and the topmost object which acquired both a linear and an angular velocity.

The formula to find the velocity of the center of mass for the object is given by:

• vo,cm = (vb,i * mb - vb,f * mb) / mo

We know the initial and final velocities of the ball (vb,i and vb,f) and the masses of the ball and object (mb and mo). Using these values, we can calculate the center of mass velocity of the object.