Example: Calculating the net force

The fan cart in the video below is observed to experience a net force to the right. Determine the (vector) net force acting on the fan cart.

You need to compute the net force on the fan cart using the information provided and any information that you can collect or assume.

• The fan cart accelerates to the right.

• The mass of the fan cart is not given, but can be found online ($m_{car} = 0.3 kg$).
• The force that the air exerts on the fan blades, which is responsible for the force to right, is unknown. This could be determined by finding the change in momentum of the fan cart over some time interval. Let's say that was done and it was found to be $F_{air} = 0.45 N$.

• The fan cart experiences several forces including the force of the air on the blades to the right, the gravitational force directly downward, the force applied by the track directly upward, some frictional forces and air resistance. Over the interval that we care about it, we will neglect the frictional forces and the force of air resistance.

• The net force acting on the fan cart is the sum of all the forces, $\vec{F}_{net} = \Sum \vec{F}_i = \vec{F}_1 + \vec{F}_2 + \dots$.

We compute the momentum vector.

$$\vec{p}_{car} = m_{car} \vec{v}_{car} = (884.05 kg) \langle 22.35, 0, 1.06\rangle\dfrac{m}{s} = \langle 1.98 \times 10^4, 0, 9.37 \times 10^2\rangle \dfrac{kg\:m}{s}$$