Physics practice problem help! A baseball of mass m1 = 0.35 kg is thrown at another ball hanging from the ceiling by a length of string…?

Question

A baseball with a mass of m1 = 0.35 kg is thrown at a second ball hanging from the ceiling by a length of string, L = 1.05 m. The second ball, with a mass of m2 = 0.62 kg, is initially at rest while the baseball has an initial horizontal velocity of V1 = 3.5 m/s. After the collision, the baseball falls straight down, leaving it with no horizontal velocity. 
a.) What is the angle that the string makes with the vertical at the highest point of travel, in degrees?

Anonymous · Accepted Answer

If you go to the following website, you will see a picture and the equation for determining the angle at the highest point.

http://dev.physicslab.org/Document.aspx?doctype=3&...

h = L – L * cos θ

h = 1.05 – 1.05 * cos θ

1.05 * cos θ = 1.05 – h

cos θ = 1 – h/1.05

To determine the maximum height, use conservation of kinetic and potential energy. As the 2nd ball rises to its maximum height, its kinetic energy is converted into potential energy.

PE = m g h, KE = ½ m v^2

m g h = ½ m v^2

h = ½ * v^2/9.8 = v^2/19.6

we need to determine the kinetic energy of the second ball after the collision. To determine the 2nd ball velocity after the collision, use conservation of momentum.

Initial momentum of 1st ball = 0.35 * 3.5 = 1.225

Since the baseball has no horizontal velocity after the collision, all of its momentum is transferred to the 2nd ball. Use the following equation to determine the initial velocity of the 2nd ball.

0.62 * v = 1.225, v = 1.225 ÷ 0.62

This is approximately 1.98 m/s.

Let’s use the velocity to determine the maximum height of the ball.

h = (1.225 ÷ 0.62)^2/19.6

This is approximately 0.2 meter

cos θ = 1 – 0.2/1.05

cos θ = 0.810310441

The angle is approximately 35.9˚.

I have a computer program called Interactive Physics. I use this program to make a computer simulation of problems like this one. The program measures, velocity, position, kinetic, and potential energy. When I ran the program, the ball’s maximum height was approximately 0.2 meter and the angle was approximately 35˚. This is my way determining if my answer is correct. I hope my work has helped you to understand how to solve this type problem. If you need help in the future, make me one of your contacts. Your questions will come directly to my yahoo email address.

[email protected]

Justen Littel DVM

Physics practice problem help! A baseball of mass m1 = 0.35 kg is thrown at another ball hanging from the ceiling by a length of string…?

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