Question

A block of mass m = 0.600 kg is pressed against a horizontal spring of elastic constant k = 20 N/m, compressing it by 20.0 cm. The block is then released. Once it loses contact with the spring, the block travels a distance 33 cm on a rough horizontal surface before it comes to a stop. What is the coefficient of kinetic friction between the block and the surface?

Answer 1

The coefficient of kinetic friction is 1.03

Step-by-step explanation:

Step 1: Given data

⇒ mass of the block = 0.600 kg

⇒ elastic constant k = 20 N/m

⇒ The spring is compressed by 20.0 cm (=x) = 0.2 m

⇒ Once it loses contact with the spring, the block travels a distance 33 cm

Step 2: Calculate the potential energy

Ep = 1/2 * k * x²

Ep = 1/2 * 20N/m * (0.2m)²

Ep = 0.4 Nm

Step 3: Calculate the coefficient of kinetic friction

At the end of the movement Potential energy = work

W = Ep = 0.4Nm = µx * m * g* x

µx = Ep / (m*g*x)

µx = 2Nm / ( 0.6 kg * 9.81 m/s² * 0.33m)

µx = 1.03

The coefficient of kinetic friction is 1.03