Question

A team of eight dogs pulls a sled with waxed wood runners on wet snow (mush!). The dogs have average masses of 20.0 kg, and the loaded sled with its rider has a mass of 245 kg. (Assume that friction is not negligible.)

(a) Calculate the acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow.
(b) Calculate the force in the coupling between the dogs and the sled.

Answer 1

Answer: (a) Acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow is 2.88
`m/s^(2)`.

(b) The force in the coupling between the dogs and the sled is 1041.74 N.

Step-by-step explanation:

(a) Formula to calculate acceleration is as follows.

`\sum F_(x) = 8F_(d) - f_(s(max))`

=
`(m_(s) + 8m_(d))a`

a =
`(8F_(d) - \mu_(s)m_(s)g)/(m_(s) + 8m_(d))`

=
`(8(185 N) - (0.14)(245)(9.8))/(245 + 8(19.0 kg))`

=
`(1480 - 336.14)/(397)`

=
`(1143.86)/(397)`

= 2.88
`m/s^(2)`

Therefore, acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow is 2.88
`m/s^(2)`.

(b) According to Newton's second law of motion we will calculate the value of T as follows.

`\sum F_(x) = T - f_(s(max)) = m_(s)a`

T =
`m_(s)a + \mu_(s)m_(s)g`

=
`245(2.88 m/s^(2)) + (0.14)(245)(9.8)`

= 705.6 + 336.14

= 1041.74 N

Therefore, we can conclude that the force in the coupling between the dogs and the sled is 1041.74 N.