Physics 2003 JAMB Past Questions - Question 2: On top of a spiral spring of force constant 500Nm-¹ is placed a mass of 5 x 10³ kg. If the spring is compressed downwards by a length of 0.02m and then released, calculate the height to which the mass is projected.

Correct Answer

B

Explanation

To calculate the height to which the mass is projected when released from the compressed spring, you can use the principle of conservation of mechanical energy. The mechanical energy of the system is conserved, so the potential energy stored in the compressed spring is converted into kinetic energy and then gravitational potential energy as the mass is projected upward.

1. Calculate the potential energy stored in the compressed spring:
 
  Potential Energy (PE_spring) = (1/2) * k * x^2

  where:
  k = force constant of the spring = 500 N/m
  x = compression distance = 0.02 m

  PE_spring = (1/2) * 500 N/m * (0.02 m)^2
  PE_spring = 0.2 J

2. When the spring is released, all of the potential energy stored in the spring is converted into kinetic energy. So, the kinetic energy of the mass when it's released from the spring is equal to the potential energy of the spring:

  Kinetic Energy (KE) = 0.2 J

3. When the mass reaches its highest point, all of its kinetic energy is converted into gravitational potential energy. So, at the highest point, the kinetic energy is zero, and the potential energy is maximum.

  Gravitational Potential Energy (PE_gravity) = m * g * h

  where:
  m = mass of the object = 5 x 10^3 kg
  g = acceleration due to gravity ≈ 9.81 m/s² (approximately)

  We want to find h (the height).

  0.2 J = (5 x 10^3 kg) * (9.81 m/s²) * h

Now, solve for h:

h = 0.2 J / [(5 x 10^3 kg) * (9.81 m/s²)]
h ≈ 0.0041 meters

So, the height to which the mass is projected when released from the compressed spring is approximately 0.0041 meters or 4.1 millimeters.