M1, C4 - Elastic Collisions in 1 Dimension

Question 1

What is the letter for the coefficient of restitution

Answer 1

e

Question 2

What is the formula for the coefficient of restitution

Answer 2

speed of separation of particles / speed of approach of particles

Question 3

What vales can e take

Answer 3

0 <= e <= 1

Question 4

What is the value of e for perfectly elastic collisions

Answer 4

1

Question 5

What is the value of e for perfectly inelastic collisions

Answer 5

0

Question 6

What do you do with v1 and v2 to find the speed of separation of two particles if they are moving towards each other

Answer 6

v1 + v2

Question 7

What do you do with v1 and v2 to find the speed of separation of two particles if they are moving away from each other
(given v2 > v1)

Answer 7

v2 - v1

Question 8

What law do you often have to use along with coefficient of restitution to find answers

Answer 8

Conservation of linear momentum

Question 9

Does the direction in momentum matter

Answer 9

YES, take velocities moving away from the +ve as -ve

Question 10

P and Q with masses 3m and 4m move towards each other with speeds 3u and 2u. Coefficient of restitution = e. Floor is smooth and horizontal, show speed of Q after collision = u/7 * (15e + 1)

Answer 10

CLM:
(3m * 3u) + (4m * -2u) = (3m * -v) + (4m * w)
u = -3v + 4w
e:
e = (v + w) / (3u + 2u) –> 5eu = v + w
v = 5eu - w
Sub in:
u = -3(5eu - w) + 4w
u = -15eu + 3w + 4w
7w = 15eu + u
w = u/7 * (15e + 1)

Question 11

You assumed v changed direction and therefore took it as -ve. Given that you were wrong and the direction of a particle remained unchanged, how do you find the possible values for e

Answer 11

Find an equation for v1
Make you v1 value negative (flip sign)

Question 12

What equation for impulse should you use to find impulse if you know the speed before and after a collision for a particle

Answer 12

I = mv - mu

Question 13

What is the equation for the coefficient of restitution for a particle colliding with a smooth wall

Answer 13

e = speed of rebound / speed of approach

Question 14

For particles dropped against the ground, how do you find the speed of approach

Answer 14

Use SUVAT to find v
Take S as the distance to the ground

Question 15

What is the formula for loss of KE

Answer 15

KE before collision - KE after collision
0.5 * m * ((u1^2 + u2^2) - (v1^2 + v2^2))

Question 16

What 4 equation can we use with elastic collision equations

Answer 16

Impulse
Conservation of linear momentum
Loss of KE
e = v / u

Question 17

v = u/4 * (-3e + 1) where v is the assumed direction of motion after a collision. Show that if the direction of collision is reversed, e > 1/3

Answer 17

v < 0 as v is now -ve
0 > u/4 * (-3e + 1)
0 > -3eu + u
-u > -3eu
-1 > -3e
1/3 < e

Question 18

How can you find the total distance travelled by an infinitely bouncing ball before coming to rest

Answer 18

Use the sum to infinity formula
a / 1 - r
Where a is term 1 and r is the common difference
(be careful that the first fall is one lot of the distance but the subsequent bounces are 2 * the peaks)