64.5k views
3 votes
A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed? *

User Roja Buck
by
8.3k points

1 Answer

4 votes

The speed of the mass is determined as 6.93 m/s.

How to calculate the speed of the mass?

The speed of the mass is calculated by applying the law of conservation of energy as follows;

Gravitational potential energy of the mass = kinetic energy of mass + elastic energy of the spring

mgh = ¹/₂mv² + ¹/₂kx²

where;

  • m is the mass
  • v is the speed of the mass
  • k is the spring constant
  • x is the extension of the spring

20 x 9.8 x 0.4 = ¹/₂ x 20 x v² + ¹/₂ x (380) x (0.4²)

78.4 = 10v² + 30.4

10v² = 78.4 - 30.4

10v² = 48

v² = 48 / 10

v² = 4.8

v = √ (4.8)

v = 6.93 m/s

User RobertoAllende
by
8.1k points