A Ball Of Mass 0.25kg Losses Half Of Its Velocity When It Makes A Head On Collision With An Identical Ball Q At Rest.After The Collision,Q Moves off with a speed of 2m/s in the original direction of p.calculate the initial velocity of p.
Consider the formula. P=mv. Due to inelastic collisions we concur an impulse logically follows. Impulse = the change of momentum.
Hence in mathematical terms:
(.25)(1/2)V = 0.5(2-V) simplify
0.125V = 1 - 0.5V simplify
0.625V = 1 Simplify
V = 1.6 m/s
.25 v = .25 (v/2) + .25 (2)
.125 v = .5
v = 4 m/s
Damon is wrong. He forgot to put 1/2*V, I think his logic was that due to the velocity = 2 m/s he automatically assume it was 4 m/s. His mathematics is flawed and you should exempt his answers from your solution sheet. The VELOCITY IS A VARIABLE YOU CANNOT ASSUME BASED UPON THE KINETIC ENERGY THAT FOLLOWS. REMEMBER DUE TO INELASTIC COLLISIONS KINETIC ENERGY IS NOT CONSERVED!!!!!!!!!!!!!!
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Gotta side with Damon on this one. KE is not conserved, but momentum is.
The answer to Richard is 1.2m/s
To calculate the initial velocity of ball P, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's break down the problem step by step:
1. Let the initial velocity of ball P be v.
2. According to the problem, ball P loses half of its velocity during the collision. Therefore, after the collision, the velocity of ball P will be 0.5v.
3. Ball Q is at rest before the collision, so its initial velocity is 0 m/s.
4. After the collision, ball Q moves off with a speed of 2 m/s in the original direction of ball P.
Now, we can apply the conservation of momentum equation:
Initial momentum of ball P + Initial momentum of ball Q = Final momentum of ball P + Final momentum of ball Q
(mass of P * initial velocity of P) + (mass of Q * initial velocity of Q) = (mass of P * final velocity of P) + (mass of Q * final velocity of Q)
(0.25 kg * v) + (0.25 kg * 0) = (0.25 kg * 0.5v) + (0.25 kg * 2 m/s)
0.25v = 0.125v + 0.5
0.375v = 0.5
v = 0.5 / 0.375
v ≈ 1.33 m/s
Therefore, the initial velocity of ball P is approximately 1.33 m/s.