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:
- External force exerted on the sled, measured in newtons.
- Friction force, measured in newtons.
- Normal force from the ground on the mass, measured in newtons.
- Weight, measured in newtons.
b) The weight of the sled is determined by the following formula:
(1)
Where:
- Mass, measured in kilograms.
- Gravitational acceleration, measured in meters per square second.
If we know that
and
, the weight of the sled is:
![W = (50\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)](https://tex.z-dn.net/?f=W%20%3D%20%2850%5C%2Ckg%29%5Ccdot%20%5Cleft%289.807%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29)
![W = 490.35\,N](https://tex.z-dn.net/?f=W%20%3D%20490.35%5C%2CN)
The weight of the sled is 490.35 newtons.
c) The minimum force needed to start the sled moving on the horizontal ground is:
(2)
Where:
- Static coefficient of friction, dimensionless.
- Weight of the sled, measured in newtons.
If we know that
and
, then the force needed to start the sled moving is:
![F_{min,s} = 0.3\cdot (490.35\,N)](https://tex.z-dn.net/?f=F_%7Bmin%2Cs%7D%20%3D%200.3%5Ccdot%20%28490.35%5C%2CN%29)
![F_{min,s} = 147.105\,N](https://tex.z-dn.net/?f=F_%7Bmin%2Cs%7D%20%3D%20147.105%5C%2CN)
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:
(3)
Where
is the kinetic coefficient of friction, dimensionless.
If we know that
and
, then the force needed to keep the sled moving at a constant velocity is:
![F_{min,k} = 0.1\cdot (490.35\,N)](https://tex.z-dn.net/?f=F_%7Bmin%2Ck%7D%20%3D%200.1%5Ccdot%20%28490.35%5C%2CN%29)
![F_{min,k} = 49.035\,N](https://tex.z-dn.net/?f=F_%7Bmin%2Ck%7D%20%3D%2049.035%5C%2CN)
A force of 49.035 newtons is needed to keep the sled moving at a constant velocity.