Answer:
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.
Explanation:
a) We kindly invite you to see below the Free Body Diagram of the forces acting on the sled. All forces are listed:
[tex]F[/tex] - External force exerted on the sled, measured in newtons.
[tex]f[/tex] - Friction force, measured in newtons.
[tex]N[/tex] - Normal force from the ground on the mass, measured in newtons.
[tex]W[/tex] - Weight, measured in newtons.
b) The weight of the sled is determined by the following formula:
[tex]W = m\cdot g[/tex] (1)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If we know that [tex]m = 50\,kg[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], the weight of the sled is:
[tex]W = (50\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]
[tex]W = 490.35\,N[/tex]
The weight of the sled is 490.35 newtons.
c) The minimum force needed to start the sled moving on the horizontal ground is:
[tex]F_{min,s} = \mu_{s}\cdot W[/tex] (2)
Where:
[tex]\mu_{s}[/tex] - Static coefficient of friction, dimensionless.
[tex]W[/tex] - Weight of the sled, measured in newtons.
If we know that [tex]\mu_{s} = 0.3[/tex] and [tex]W = 490.35\,N[/tex], then the force needed to start the sled moving is:
[tex]F_{min,s} = 0.3\cdot (490.35\,N)[/tex]
[tex]F_{min,s} = 147.105\,N[/tex]
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:
[tex]F_{min,k} = \mu_{k}\cdot W[/tex] (3)
Where [tex]\mu_{k}[/tex] is the kinetic coefficient of friction, dimensionless.
If we know that [tex]\mu_{k} = 0.1[/tex] and [tex]W = 490.35\,N[/tex], then the force needed to keep the sled moving at a constant velocity is:
[tex]F_{min,k} = 0.1\cdot (490.35\,N)[/tex]
[tex]F_{min,k} = 49.035\,N[/tex]
A force of 49.035 newtons is needed to keep the sled moving at a constant velocity.
