Question

A 5.5 g coin sliding to the right at 21.0 cm/s makes an elastic head-on collision with a 16.5 g coin that is initially at rest. After the collision, the 5.5 g coin moves to the left at 10.5 cm/s. (a) Find the final velocity of the other coin. cm/s (b) Find the amount of kinetic energy transferred to the 16.5 g coin. J

Answer 1

(a) 0.105 m/s

(b) 9.096×10⁻⁵ J

Step-by-step explanation:

(a)

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

mu+m'u' = mv+m'v'......................... Equation 1

Where m = mass of the first coin, m' = mass of the second coin, u = initial velocity of the first coin, u' = initial velocity of the second coin, v = final velocity of the first coin, v' = final velocity of the second coin.

Given: m = 5.5 g = 0.0055 kg, m' = 16.5 g = 0.0165 kg, u = 21.0 cm/s = 0.21 m/s, u' = 0 m/s (at rest), v = 10.5 cm/s = -0.105 m/s (to the left)

Substitute into equation 1

0.0055(0.21)+0.00165(0) = 0.0055(-0.105)+0.0165(v')

0.001155 = -0.0005775+0.0165v'

0.001155+0.0005775 = 0.0165v'

v' = 0.0017325/0.0165

v' = 0.105 m/s

(b) The amount of kinetic energy transferred to the 16.5 g coin is given as

Ek = 1/2m'v'²+1/2m'u'²........................... Equation 2

Given: m' = 0.0165 kg, v' = 0.105 m/s, u' = 0 m/s

Substitute into equation 2

Ek = 1/2(0.0165)(0.105²)- 1/2(0.0165)(0²)

Ek = 1/2(0.0165)(0.011025)-0

Ek = 9.096×10⁻⁵ J

Answer 2

(a) 10.33 cm/s

(b) 0.00088 J

Step-by-step explanation:

Parameters given:

Mass of first coin, m = 5.5g = 0.0055kg

Mass of second coin, M = 16.5 = 0.0165kg

Initial velocity of first coin, u = 21 cm/s

Final velocity of first coin, v = -10cm/s (because it's in the opposite direction of the initial motion)

Initial velocity of second coin, U = 0 cm/s

(a) Using principle of conservation of momentum:

Total initial momentum = Total final momentum

m*u + M*U = m*v + M*V

U = 0

=> m*u + 0 = m*v + M*V

m*u - m*v = M*V

V = m(u - V) / M

V = 0.0055(21 - (-10)) / 0.0165

V = 0.3333 * 31 = 10.33 cm/s

(b) Kinetic energy is given as:

KE = 0.5 * M * V²

V = 10.33 cm/s = 0.1033 m/s

KE = 0.5 * 0.0165 * 0.1033²

KE = 0.00088 J