A spring with k = 50 N/m is attached to a 2 kg mass on a frictionless surface. The mass is displaced by x = 0.2 m from equilibrium. What is the restoring force, and what is the resulting acceleration?

A spring with k = 50 N/m is attached to a 2 kg mass on a frictionless surface. The mass is displaced by x = 0.2 m from equilibrium. What is the restoring force, and what is the resulting acceleration?

• A. F = -10 N; a = -5 m/s^2
• B. F = 10 N; a = 5 m/s^2
• C. F = -20 N; a = -10 m/s^2
• D. F = -5 N; a = -2.5 m/s^2

Answer: (A)

The main idea being tested is using Hooke’s law and Newton’s second law together. A spring exerts a restoring force toward equilibrium given by F = -kx, and the resulting acceleration is a = F/m. With k = 50 N/m and the mass displaced by x = 0.2 m, the restoring force is F = -kx = -(50)(0.2) = -10 N. The negative sign shows the force acts toward the equilibrium position. Then use F = ma to find the acceleration: a = F/m = (-10 N) / (2 kg) = -5 m/s^2. The negative sign again indicates acceleration toward equilibrium. So the correct description is a restoring force of -10 N and an acceleration of -5 m/s^2. The other options would require either a sign that points away from equilibrium or magnitudes not consistent with the given displacement or mass.

The main idea being tested is using Hooke’s law and Newton’s second law together. A spring exerts a restoring force toward equilibrium given by F = -kx, and the resulting acceleration is a = F/m.

With k = 50 N/m and the mass displaced by x = 0.2 m, the restoring force is F = -kx = -(50)(0.2) = -10 N. The negative sign shows the force acts toward the equilibrium position.

Then use F = ma to find the acceleration: a = F/m = (-10 N) / (2 kg) = -5 m/s^2. The negative sign again indicates acceleration toward equilibrium.

So the correct description is a restoring force of -10 N and an acceleration of -5 m/s^2. The other options would require either a sign that points away from equilibrium or magnitudes not consistent with the given displacement or mass.