A solid block of mass 16 kg slides down a ramp from a height of 4.9 m on to a smooth horizontal floor where it encounters a frictional force of 38.2 N. Using the principles of mechanical energies, and the work done by dissipative forces like friction, calculate how long is the distance traveled across the floor until it comes to a stop?

(Assume g=9.8 and the mass of the block is needed for this calculation)

The distance travel across the floor is 20.11 m.

the velocity of the block down the ramp is calculated as

v=√2gh

here, h is the ramp height

v=√ (2*9.81*4.9) = 9.8 m/s

Now according the law of energy conservation, the kinetic energy of the block would be used to overcome the friction force, and move the block.

let the distance move by the block is "d"

Kinetic energy = Work done to over come friction

0.5mv²=F*d

0.5*16*9.8²=38.2*d

d=20.11 m