Answer:
1.21 m/s
Explanation:
From the law of conservation of energy,
U₁ + K₁ + E₁ = U₂ + K₂ + E₂
where U₁ = initial potential energy of system =initial potential energy of still ball = mgh where m = mass of still ball = 0.514 kg, g = acceleration due to gravity = 9.8 m/s² and h = height = length of cord = 68.7 cm = 0.687 m.
K₁ = initial kinetic energy of system = 0
E₁ = initial internal energy of system = unknown and
U₂ = final potential energy of system = 0
K₁ = final kinetic energy of system = final kinetic energy of ball + steel block = 1/2(m + M)v² where m = mass of still ball, M = mass of steel block = 2.63 kg and v = speed of still ball + steel block
E₁ = final internal energy of system = unknown
So,
U₁ + K₁ + E₁ = U₂ + K₂ + E₂
mgh + 0 + E₁ = 0 + 1/2(m + M)v² + E₂
mgh = 1/2(m + M)v² + (E₂ - E₁)
Given that (E₂ - E₁) = change in internal energy = ΔE = 1/2ΔK where ΔK = change in kinetic energy. So, ΔE = 1/2ΔK = 1/2(K₂ - K₁) = K₂/2 = 1/2(m + M)v²/2 = (m + M)v²/4
Thus, mgh = 1/2(m + M)v² + (E₂ - E₁)
mgh = 1/2(m + M)v² + (m + M)v²/4
mgh = 3(m + M)v²/4
So, making v subject of the formula, we have
v² = 4mgh/3(m + M)
taking square root of both sides, we have
v = √[4mgh/3(m + M)]
Substituting the values of the variables into the equation, we have
v = √[4 × 0.514 kg × 9.8 m/s² × 0.687 m/{3(0.514 kg + 2.63 kg)}]
v = √[13.8422/{3(3.144 kg)}]
v = √[13.8422 kgm/s²/{9.432 kg)}]
v = √(1.4676 m²/s²)
v = 1.21 m/s
