# Find Maximum Angle: Ball Hitting Pendulum String

• robbondo
In summary, the conversation discusses the calculation of the maximum angle at which a block will swing after being hit by a ball with a certain initial velocity. The equations used include conservation of momentum and energy. One member suggests using energy conservation to solve the problem, while another member points out that the other ball carries away some of the kinetic energy. The original poster then revises their equation to account for this and asks for confirmation of their solution.

## Homework Statement

A ball with mass m with an initial velocity of 5 m/s strikes a ball with a mass of 3m hanging at rest from a string 50 cm long. Find the maximum angle(x) with which the block swings after its hit.

k=1/2mv^2
p=mv

## The Attempt at a Solution

Well first I solved the momentum

mAvA1+mBvB1=mAvA2+mBvB2

to get vB2=5-vA2

Then I used conservation of energy to get

[tex]sqrt {25 - v_{A2}/3} [\tex]

I solved the two equations for vB2 and got 3.53 m/s

So, since the kinetic energy from the start of the mass on the pendelum moving to its peak is h=(.5-.5cosx)

1/2m(vB2^2)=mg(.5-.5cosx)

I solved for the angle and got 50.2 degrees.

Anyone see anything wrong with my math or my logic? I can only attempt the problem one more time before the program gives me no credit.

Couldn't you just use energy conservation, since the block's kinetic energy at the maximal angle equals zero? It posesses only potential energy at that point, and at the impact point, there is only kinetic energy from the ball.

Couldn't you just use energy conservation, since the block's kinetic energy at the maximal angle equals zero? It posesses only potential energy at that point, and at the impact point, there is only kinetic energy from the ball.

The other ball carries away some of the kinetic energy. I think he's doing it right. I haven't checked the answer though.

Dick said:
The other ball carries away some of the kinetic energy. I think he's doing it right. I haven't checked the answer though.

Good point, so after reconsidering...

robbondo said:
Well first I solved the momentum

mAvA1+mBvB1=mAvA2+mBvB2

to get vB2=5-vA2

...shouldn't this be VB2 = (5 - VA2)/3 ?

## 1. What is the maximum angle at which the ball can hit the pendulum string?

The maximum angle at which the ball can hit the pendulum string is dependent on various factors such as the length and weight of the pendulum string, the mass and velocity of the ball, and the force of gravity. A mathematical equation can be used to calculate the maximum angle, which is often referred to as the critical angle.

## 2. How does the maximum angle affect the motion of the pendulum?

The maximum angle at which the ball hits the pendulum string affects the motion of the pendulum by determining the amplitude and period of the pendulum's oscillations. A higher maximum angle would result in a larger amplitude and longer period, while a lower maximum angle would result in a smaller amplitude and shorter period.

## 3. Can the maximum angle be exceeded?

Yes, the maximum angle can be exceeded if the ball is given enough initial velocity. However, this would result in the pendulum string breaking or the ball bouncing off the string, disrupting the motion of the pendulum. Therefore, it is important to calculate and maintain the maximum angle to ensure the stability of the pendulum's motion.

## 4. How does the maximum angle change with different variables?

The maximum angle can change with different variables such as the length and weight of the pendulum string, the mass and velocity of the ball, and the force of gravity. For example, a longer pendulum string would result in a smaller maximum angle, while a heavier ball would result in a larger maximum angle. These variables can be manipulated to achieve different maximum angles and alter the motion of the pendulum.

## 5. What are the real-world applications of finding the maximum angle of a ball hitting a pendulum string?

The concept of finding the maximum angle of a ball hitting a pendulum string has various real-world applications, such as in amusement park rides, clock mechanisms, and seismometers. It is also used in physics experiments to study the motion of pendulums and the effects of different variables on the maximum angle and the resulting motion.