A loaded 320 kg toboggan is traveling on smooth horizontal snow at 4.60 m/s when it suddenly comes to a rough region. The region is 8.60 m long and reduces the toboggan's speed by 1.20 m/s. What average friction force did the rough region exert on the toboggan?

367.04 N

Explanation:

Frictional force = mass of the toboggan*deceleration caused by the rough region

Fr = m*ar ... Equation 1

Where Fr = Average frictional force, m = mass of loaded toboggan, ar = deceleration cause by the rough region.

We can calculate for ar using the formula below

v² = u²+2ars ... Equation 2

make ar the subject of the equation

ar = (v²-u²) / 2s ... Equation 3

Where v = final velocity of the toboggan, u = initial velocity of the toboggan, s = distance or length of the rough region

Given: v = 1.2 m/s, u = 4.6 m/s, s = 8.6 m

Substitute into equation 3

ar = (1.2²-4.6²) / (2*8.6)

ar = (1.44-21.16) / 17.2

ar = - 19.72/17.2

ar = - 1.147 m/s²

Also given: m = 320 kg

Substitute into equation 1

Fr = 320 (-1.147)

Fr = - 367.04 N

Note: The negative sign tells that the frictional force opposes the motion of the toboggan