Question

using energy: a mass, m1 = 5kg, resting on a frictionless ramp is connected to a cable that passes over a pulley which is then attached to a second hanging mass, m2 = 2. see diagram. if the blocks are released from rest, then how far will the have moved when their velocities are 4 m/s

Answer 1

Given that :

mass of the block 1, m₁ = 5 kg

mass of the block 2, m₂ = 2 kg

According to figure, we have

T = m₁ a                                                   { eq.1 }

and   m₂ g - T = m₂ a                                                    { eq.2 }

equating above two equations, we get

m₂ g - m₁ a = m₂ a     

m₂ g = a ( m₁ + m₂)

or   a = m₂ g / ( m₁ + m₂)                                                             { eq.3 }

where, g = acceleration due to gravity = 9.8 m/s²

inserting the values in eq.3,

a = (2 kg) (9.8 m/s²) [(5 kg) + (2 kg)

a = (19.6 kg.m/s²) / (7 kg)

a = 2.8 m/s²

if the blocks are released from rest, then distance travelled to be moved when their velocities are 4 m/s which is given as :

using equation of motion 3,

v² = v₀² + 2 a d                                                              { eq.4 }

where, v₀ = 0 m/s

inserting the values in eq.4,

(4 m/s)² = (0 m/s)² + 2 (2.8 m/s²) d

(16 m²/s²) = (5.6 m/s²) d

d = 2.85 m