A steel cable lying flat on the floor drags a 20 kg block across a horizontal, frictionless floor. A 110 N force applied to the cable causes the block to reach a speed of 3.9 m/s at a distance of 1.9 m. What is the mass of the cable?

The answer is;

The mass of the cable is 7.428 kg

Explanation:

Force = 110 N

Mass of block = 20 kg

velocity = 3.9 m/s

We apply the law of motion which is

v² = u² + 2·a·s

Where a = acceleration

s = distance = 1.9 m and

u = initial velocity = 0 m/s

v = velocity = 3.9 m/s

∴ v² = 2·a·s

3.9² = 2*1.9*a which gives

a = 4.003 m/s²

F = m*a

Where F = Force = 110 N

m = mass

a = acceleration = 4.003 m/s²

∴ m = F/a = 110/4.003 = 27.482 kg

Since the mass of the block = 20 kg

Mass of cable + block = 27.482 kg

Mass of cable = 27.428 kg - mass of block = 27.428 kg - 20 kg = 7.428 kg

Mass of cable = 7.428 kg