A mass M = 1.4 kg is hanging from a long string of length L-20.8 m and total mass mi = 13 kg. A student gives the mass a quick horizontal shake to set up a wave which travels upwards along the string 25% Part (a) What is the speed of the wave at the bottom of the string, in meters per second? 25% Part (b) Express the tension of the chain at a height y above the bottom in terms of M, m, and g 25% Part (c) What is the speed of the wave, in meters per second, at the top of the string?

a. v = 4.68 m/s²

b. T₂ = 141.12 N

c. v = 15.02 m/s²

Explanation:

Given:

M = 1.4 kg, L = 20.8m, mi=13 kg

a.

Using the equations of kinetic energy and the spring potential

Uk = Ek

¹/₂ * T * d = ¹/₂ * m * v ²

T₁ = M * g = 1.4 kg * 9.8 m/s² = 13.72 N

T₂ = (M + mi) * g = (1.4 kg + 13 kg) * 9.8 m/s² = 141.12 N

a. the speed at the bottom

v = √[ (T * d) / m] = √ 13.72 N * 20.8 m / 13 kg

v = 4.68 m/s²

b. the tension of the chain

T₂ = (M + mi) * g = (1.4 kg + 13 kg) * 9.8 m/s² = 141.12 N

c. the speed at the top of the spring

v = √[ (T * d) / m] = √ 141.12 N * 20.8 m / 13 kg

v = 15.02 m/s²