What is the Initial Velocity v0 in a Perfectly Elastic Collision?

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Homework Help Overview

The problem involves a perfectly elastic collision between a 15 g ball and a 117 g ball, where the first ball is fired horizontally and the second is hanging from a string. After the collision, the second ball swings to a maximum angle of 53°. The objective is to determine the initial velocity v0 of the first ball.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the appropriate equations for kinetic energy and the relationship between the angle and height in the context of the swinging ball. There is uncertainty about whether the angle should be adjusted before use in calculations.

Discussion Status

Some participants have offered insights into the equations related to kinetic energy and the geometry of the problem. There is an ongoing exploration of how to correctly apply these equations, particularly regarding the roles of the masses involved and the conservation principles. Multiple interpretations of the setup and calculations are being considered.

Contextual Notes

Participants are navigating potential confusion regarding the definitions of the masses in the equations and the implications of the angle given in the problem. There is acknowledgment of a typo in the mass identification, which may affect the understanding of the equations being used.

sktgurl930
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Homework Statement


A 15 g ball is fired horizontally with speed v0 toward a 117 g ball hanging motionless from a 1.53-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 117 g ball swings out to a maximum angle θmax=53°. What was v0?

Homework Equations


h=L(L-cos(theta)
V=Square root of (m*g*h/(.5*M) little m is ball moving and M is the ball not moving
(v2x)f=2m1/m1+m2 (V1x)i



The Attempt at a Solution


Im not sure if I am using the right equations and whether the angle given is the one we use in the equation, or if we have to subtract it from 90 first
 
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sktgurl930 said:

Homework Statement


A 15 g ball is fired horizontally with speed v0 toward a 117 g ball hanging motionless from a 1.53-m-long string. The balls undergo a head-on, perfectly elastic collision, after which the 117 g ball swings out to a maximum angle θmax=53°. What was v0?

2. Homework Equations
h=L(L-cos(theta)
V=Square root of (m*g*h/(.5*M) little m is ball moving and M is the ball not moving
(v2x)f=2m1/m1+m2 (V1x)i

The Attempt at a Solution


Im not sure if I am using the right equations and whether the angle given is the one we use in the equation, or if we have to subtract it from 90 first

A couple of things.

Initial KE is 1/2*m*v2

The second is that the angle because it is hanging is with the vertical. Hence the height should be given by the Cosθ times the string length subtracted from the length. (h = length - projection of the string to the vertical.)

So ... 1/2*m1*v2 = m2*g*(L - L*cos53)

v2 = 2*(m2/m1)*g*(L-L*Cos53)
 
LowlyPion said:
A couple of things.

Initial KE is 1/2*m*v2

The second is that the angle because it is hanging is with the vertical. Hence the height should be given by the Cosθ times the string length subtracted from the length. (h = length - projection of the string to the vertical.)

So ... 1/2*m1*v2 = m2*g*(L - L*cos53)

v2 = 2*(m2/m1)*g*(L-L*Cos53)

so my mass 1 is the ball not moving right??
is this the equation i use to get the answer or do i have to plug it into another one
 
sktgurl930 said:
so my mass 1 is the ball not moving right??
is this the equation i use to get the answer or do i have to plug it into another one

Sorry my mistake. The m1 I wrote on the left should be m2 - the stationary ball. We are trying to calculate the velocity of m2 AFTER impact. The m's should cancel there. Sorry for my typo which I then proceeded to run with.

With that final velocity for the stationary ball after impact and the usual equations for conservation of energy and momentum, you should now have 2 equations and 2 unknowns, one of which is the Vo that they ask for.
 

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