A weightless spring with a stiffness of 40 N / m is attached to a bar weighing 1 kg. The coefficient of friction between

A weightless spring with a stiffness of 40 N / m is attached to a bar weighing 1 kg. The coefficient of friction between the bar and the horizontal surface is 0.8. If at first the spring is not deformed, then work must be done to evenly move the bar by 2 m.

Given:

m = 1 kg is the mass of the bar;

k = 40 N / m – coefficient of spring stiffness;

n = 0.8 is the coefficient of friction between the bar and the surface;

g = 10 m / s ^ 2 – acceleration of gravity;

l = 2 meters – the length of the movement.

It is required to find work A (Joule), which must be done to move the bar at a distance l.

To move the bar, it is necessary to overcome the elastic force Fу of the spring and the friction force Ffr, the final force that must be applied to the bar will be equal to:

F = Fу + Ftr = k * l + n * m * g = 40 * 2 + 0.8 * 1 * 10 = 80 + 8 = 88 Newtons.

A = F * l = 88 * 2 = 176 Joules.

Answer: To move the bar, you need to do work equal to 176 Joules.