Question

You push a 50 kg wooden box across a wooden floor at a constant speed of 1.0 m/s. The coefficient of kinetic friction is 0.15. Now you double the force on the box. How long would it take for the velocity of the crate to double to 2.0 m/s?

Answer 1

0.68 seconds

Step-by-step explanation:

Data provided in the question:

Mass of the box = 50 kg

Speed of the box = 1.0 m/s

Coefficient of friction, μ = 0.15

Now,

Force applied = μmg

Here,

g is the acceleration due to gravity = 9.8 m/s²

Thus,

F = 0.15 × 50 × 9.8

= 73.5 N

Also,

Force = Mass × Acceleration

thus,

73.5 N = 50 × a

or

a = 1.47 m/s²

After doubling the speed

Final speed = 2 × Initial speed

= 2 × 1 m/s

= 2 m/s

Also,

Acceleration = [change in speed] ÷ Time

or

1.47 = [ 2 - 1 ] ÷ Time

or

Time = 1 ÷ 1.47

or

Time = 0.68 seconds