Question about the solution to this elastic collision

In summary, the equations 1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2 and m1v1i+mvv2i=m1v1f+m2v2f are not interchangeable as they give different answers. Collisions conserve momentum but not necessarily energy, so one should default to momentum conservation unless told that the collision is perfectly elastic. Using both equations may involve solving for two unknowns.
  • #1
as2528
40
9
Homework Statement
High-speed stroboscopic photographs show that the
head of a golf club of mass 200 g is traveling at 55.0 m/s
just before it strikes a 46.0-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just
after impact
Relevant Equations
1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2
m1v1i+mvv2i=m1v1f+m2v2f
I found that 1/2m1v1i^2+1/2m2v2i^2=1/2m1v1f^2+1/2m2v2f^2
=>0.5*200*55^2+0.5*46*0^2=0.5*40^2*200+0.5*46*0*vf^2=>vf=78.713 m/s.

The true answer is 65.2 m/s and is solved using m1v1i+mvv2i=m1v1f+m2v2f. Are these equations not interchangeable? Why can I not use the equation I used?
 
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  • #2
The equations are not interchangeable. If they were, they would give the same answer. All collisions conserve momentum but not necessarily energy.
 
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  • #3
kuruman said:
The equations are not interchangeable. If they were, they would give the same answer. All collisions conserve momentum but not necessarily energy.
I see. So the kinetic energy one works if energy is conserved? And should I always default to momentum?
 
  • #4
as2528 said:
I see. So the kinetic energy one works if energy is conserved? And should I always default to momentum?
Yes, in a collision you default to momentum conservation. If you are told that the collision is perfectly elastic, then you can use energy conservation as well. Using both, usually involves questions where there are two unknowns.
 
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  • #5
kuruman said:
Yes, in a collision you default to momentum conservation. If you are told that the collision is perfectly elastic, then you can use energy conservation as well. Using both, usually involves questions where there are two unknowns.
Thank you! This really cleared it up for me.
 
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1. What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the total energy of the system before the collision is equal to the total energy after the collision.

2. How is the velocity of the objects involved in an elastic collision calculated?

The velocity of the objects involved in an elastic collision can be calculated using the conservation of momentum and the conservation of kinetic energy equations. These equations take into account the masses and velocities of the objects before and after the collision.

3. What is the difference between an elastic collision and an inelastic collision?

In an elastic collision, the total kinetic energy of the system is conserved, while in an inelastic collision, some of the kinetic energy is lost in the form of heat, sound, or deformation of the objects involved.

4. How does the coefficient of restitution affect an elastic collision?

The coefficient of restitution is a measure of the elasticity of a collision. It is equal to the ratio of the final relative velocity to the initial relative velocity. In an elastic collision, the coefficient of restitution is equal to 1, meaning that the objects bounce off each other with no loss of kinetic energy. In a perfectly inelastic collision, the coefficient of restitution is equal to 0, meaning that the objects stick together after the collision.

5. Can an elastic collision occur between objects of different masses?

Yes, an elastic collision can occur between objects of different masses as long as the total kinetic energy of the system is conserved. The velocities of the objects will change according to the conservation of momentum and kinetic energy equations.

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