Question

A sled of mass 50 kg is pulled along a snow-covered, flat ground. The static friction coefficient is 0.3 and the kinetic friction coefficient is 0.1.

Draw a FBD of all the forces acting on the sled.
What is the weight of the sled?
What force is needed to start the sled moving?
What force is needed to keep the sled moving at a constant velocity?

Answer 1

a) We kindly invite you to see below the Free Body Diagram of the forces acting on the sled.

b) The weight of the sled is 490.35 newtons.

c) A force of 147.105 newtons is needed to start the sled moving.

d) A force of 49.035 newtons is needed to keep the sled moving at a constant velocity.

Step-by-step explanation:

a) We kindly invite you to see below the Free Body Diagram of the forces acting on the sled. All forces are listed:

`F` - External force exerted on the sled, measured in newtons.

`f` - Friction force, measured in newtons.

`N` - Normal force from the ground on the mass, measured in newtons.

`W` - Weight, measured in newtons.

b) The weight of the sled is determined by the following formula:

`W = m\cdot g` (1)

Where:

`m` - Mass, measured in kilograms.

`g` - Gravitational acceleration, measured in meters per square second.

If we know that
`m = 50\,kg` and
`g = 9.807\,(m)/(s^(2))`, the weight of the sled is:

`W = (50\,kg)\cdot \left(9.807\,(m)/(s^(2)) \right)`

`W = 490.35\,N`

The weight of the sled is 490.35 newtons.

c) The minimum force needed to start the sled moving on the horizontal ground is:

`F_(min,s) = \mu_(s)\cdot W` (2)

Where:

`\mu_(s)` - Static coefficient of friction, dimensionless.

`W` - Weight of the sled, measured in newtons.

If we know that
`\mu_(s) = 0.3` and
`W = 490.35\,N`, then the force needed to start the sled moving is:

`F_(min,s) = 0.3\cdot (490.35\,N)`

`F_(min,s) = 147.105\,N`

A force of 147.105 newtons is needed to start the sled moving.

d) The minimum force needed to keep the sled moving at constant velocity is:

`F_(min,k) = \mu_(k)\cdot W` (3)

Where
`\mu_(k)` is the kinetic coefficient of friction, dimensionless.

If we know that
`\mu_(k) = 0.1` and
`W = 490.35\,N`, then the force needed to keep the sled moving at a constant velocity is:

`F_(min,k) = 0.1\cdot (490.35\,N)`

`F_(min,k) = 49.035\,N`

A force of 49.035 newtons is needed to keep the sled moving at a constant velocity.