Question

You are pushing a sled in which your little sister is seated up a 26° slope (one that makes an angle of 26° with the horizontal). If the mass of the sled and girl is 46 kg, and the coefficient of kinetic friction between the sled and the surface is 0.100, with what force (in N) do you need to push in order for the sled to move with constant velocity?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the sled and the girl = m = 46 kg

Angle of the slope = = 26^o

Force with which you push the sled = F

Normal force on the sled from the slope = N

Coefficient of kinetic friction between the sled and the slope = = 0.1

Friction force on the sled = f

f = N

The sled is moving at constant velocity therefore the acceleration of the sled is zero.

The net force on the sled is zero therefore all the forces on it are balanced.

From the free body diagram,

N = mgCos

f = mgCos

F = mgSin + f

F = mgSin + mgCos

F = mg(Sin + Cos)

F = (46)(9.81)[Sin(26) + (0.1)Cos(26)]

F = 238.4 N

Force with which you need to push in order for the sled to move with constant velocity = 238.4 N