# Three dimensional collision with bowling ball and pin.

• unrulypanda
In summary: The Attempt at a SolutionI have no idea how to even attempt this problem.Try writing down your Conservation of Momentum equationsShould I write down the formula first? Should I plug in the numbers and continue trying to cancel out unknown variables? The conservation of energy and momentum equations are realllllly long -_-I would like too bump this-I have the same question!I tried so far using the p=mv equation in both dimensions (since in the x direction it equals zero!), however I can't seem to solve for what they're asking…my algebraic manipulations aren't as well.You might try solving for vp in terms of the λ and R variables, then using those values

## Homework Statement

In order to convert a tough split in bowling, it is necessary to strike the pin a glancing blow as shown in the figure. Assume that the bowling ball, initially traveling at 15.0 m/s, has eight times the mass of a pin and that the pin goes off at 75° from the original direction of the ball.

(a) Calculate the speed of the pin.
(b) Calculate the speed of the ball just after collision.
(c) Calculate the angle θ through which the ball was deflected. Assume the collision is elastic and ignore any spin of the ball.

## Homework Equations

MbVb+MpVp=MbVB+MpVP (Mb=mass of ball, Mp=mass of pin, Vp=initial velocity for pin, VP=final velocity for pin, Vb=initial velocity for ball, VB=final velocity for ball.)

## The Attempt at a Solution

I have no idea how to even attempt this problem.

Try writing down your Conservation of Momentum equations

Should I write down the formula first? Should I plug in the numbers and continue trying to cancel out unknown variables? The conservation of energy and momentum equations are realllllly long -_-

I would like too bump this-I have the same question!
I tried so far using the p=mv equation in both dimensions (since in the x direction it equals zero!), however I can't seem to solve for what they're asking…my algebraic manipulations aren't as well.

This is in the homework section and the forum requires you to show your working/attempt. How else can we see where you are going wrong ;-)

unrulypanda said:
Should I write down the formula first? Should I plug in the numbers and continue trying to cancel out unknown variables? The conservation of energy and momentum equations are realllllly long -_-

It's not usually a good ide to plug in the numbers early on.

unrulypanda said:
the bowling ball, initially traveling at 15.0 m/s, has eight times the mass of a pin and that the pin goes off at 75° from the original direction of the ball.
Hi, I do not know if the formula for balls is valid for pins, if it is ...then
you know cos λp (75°) = 0.2588 and the ratio Rm of Mb to total mass 8/9
you get quickly vp = v0* cos λ* 2R (15*0.25*16/9) = 6.9 m/s
the you can easily find all missing data (with the E and p formulas.)

The problem statement contains no information on the vertical dimension so this is really a 2D problem.

## 1. How does the collision between a bowling ball and pin affect the motion of both objects?

The collision between a bowling ball and pin is an example of an elastic collision, meaning that both objects maintain their shape and kinetic energy after the collision. However, the bowling ball will transfer some of its kinetic energy to the pin, causing it to move in the direction of the ball's initial motion. This is due to the conservation of momentum, where the total momentum of the system remains constant.

## 2. What factors affect the outcome of a collision between a bowling ball and pin?

The outcome of the collision between a bowling ball and pin depends on various factors such as the mass and velocity of both objects, the angle and direction of the collision, and the surface properties of the objects. These factors can influence the amount of kinetic energy transferred and the resulting motion of the objects after the collision.

## 3. How is the coefficient of restitution related to the collision between a bowling ball and pin?

The coefficient of restitution is a measure of the elasticity of a collision, and it is directly related to the collision between a bowling ball and pin. A higher coefficient of restitution means that the objects will bounce off each other with less energy loss, resulting in a more elastic collision. In contrast, a lower coefficient of restitution means that the objects will stick together or move together after the collision, resulting in a more inelastic collision.

## 4. Can the collision between a bowling ball and pin be accurately modeled using physics principles?

Yes, the collision between a bowling ball and pin can be accurately modeled using physics principles such as conservation of momentum and energy. By considering the initial conditions and properties of the objects involved, scientists can predict the outcome of the collision and verify their predictions through experiments.

## 5. How does the shape of the bowling ball and pin affect the collision?

The shape of the bowling ball and pin can affect the collision in several ways. For example, if the pin has a triangular shape, it may roll or rotate after the collision, whereas a spherical pin may only move in the direction of the ball's initial motion. Additionally, the shape of the objects can also affect the coefficient of restitution and the amount of energy transferred during the collision, ultimately impacting the outcome of the collision.