Dynamics - Another collision question

In summary, the conversation is discussing a problem involving a ram colliding with a pile and the calculation of its kinetic energy and momentum. One person makes a mistake in assuming that kinetic energy is conserved, but the other person corrects them by pointing out that momentum is conserved instead. After making the correction, they arrive at the correct answer of 7.23 m/s for the velocity of the ram.
  • #1
Chantry09
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0

Homework Statement



http://img291.imageshack.us/img291/7829/collisionok5.jpg

Homework Equations



Conservation of momentum
Conservation of Kinetic Energy
GPE
KE

The Attempt at a Solution



Ive done the first part of the question. With the second part, i thought about it this way:

If the ram is seen to have zero velocity just after impact then all of the rams kinetic energy must have been transphered to the pile, no?

In which case, having worked out the gravitational potential energy in the ram initially to be 5886J. The kinetic energy in the pile must be:

5886 = 0.5 x 300 x V^2
39.24 = V^2
6.26 = V

However apparently the answer *should* be 7.23 m/s.

Can someone tell me where i have gone wrong?

James
 
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  • #2
Your mistake is in assuming that KE is conserved.
 
  • #3
Ok. I worked out that the block would be traveling at 5.42m/s when it strikes the pile (using V^2= U^2 + 2as).

Now i know original momentum of the ram = 400 x 5.42 = 2168
Now if momentum is conservered: 2168 = 300 x V
V = 7.23 m/s

Oh, that's right...whoops. Thank you.
 

1. What is the equation for calculating momentum in a collision?

In a collision where objects have masses m1 and m2 and velocities u1 and u2 before the collision, and v1 and v2 after the collision, the equation for calculating momentum is:
m1u1 + m2u2 = m1v1 + m2v2. This equation follows the principle of conservation of momentum, which states that the total momentum of a closed system remains constant.

2. What is an elastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. This means that the objects involved in the collision do not lose any energy to other forms, such as heat or sound. In an ideal elastic collision, the objects rebound from each other with the same velocities they had before the collision.

3. How is the coefficient of restitution related to collisions?

The coefficient of restitution (e) is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between two colliding objects. In other words, it is a measure of how "bouncy" a collision is. For a perfectly elastic collision, e would equal 1, while for a completely inelastic collision, e would equal 0.

4. What is the difference between an inelastic and a completely inelastic collision?

In an inelastic collision, some kinetic energy is lost to other forms, such as heat or sound. However, the objects involved do not stick together after the collision. On the other hand, in a completely inelastic collision, the objects do stick together after the collision and move with a common velocity. In both cases, momentum is conserved, but only in an inelastic collision is kinetic energy not conserved.

5. How does the mass of an object affect the outcome of a collision?

The mass of an object affects the outcome of a collision in two ways. First, the more massive an object is, the more difficult it is to change its velocity. This means that in a collision, a more massive object will experience less change in velocity compared to a less massive object. Second, according to the principle of conservation of momentum, the total momentum of a closed system remains constant. This means that in a collision, a more massive object will transfer more momentum to the other object involved, causing it to change its velocity more significantly.

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