Question

In a circus performance, a monkey on a sled is given an initial speed of 4 m/s up a 25° incline. The combined mass of

the monkey and the sled is 20kg and the coefficient of friction between the sled and the incline is 0.20. How far up
the incline do the monkey and sled move?

Answer 1

The monkey and sled travel 3.38 meters up the incline.

Define the variables:

Initial speed (
`v_(initial)`) = 4 m/s

Mass (m) = 20 kg

Angle of incline (θ) = 25°

Coefficient of friction (μ) = 0.20

Distance traveled (d) = unknown

Convert the angle to radians:

`\theta_(rad)` = θ * π / 180°

`\theta_(rad)` ≈ 0.436 radians

Calculate the acceleration due to gravity:

g = 9.81 m/s^2

Calculate the component of gravity parallel to the incline:

`g_(parallel)` = g * sin(θ_rad)

`g_(parallel)` ≈ 4.23 m/s^2

Calculate the frictional force:

`f_(friction)` = μ * m * g * cos(
`\theta_(rad)`)

`f_(friction)` ≈ 39.2 N

Calculate the net force acting on the monkey and sled:

`f_(net)` = m *
`g_(parallel)` -
`f_(friction)`

`f_(net)` ≈ 2.43 N

Calculate the acceleration:

a =
`f_(net)` / m

a ≈ 0.1215 m/
`s^2`

Use the kinematic equation to calculate the distance traveled:

d =
`v_(initial)^2` / (2 * a)

d ≈ 3.38 meters