Answer:
(a) 10.33 cm/s
(b) 0.00088 J
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
Answer:
(a) 0.105 m/s
(b) 9.096×10⁻⁵ J
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
