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--- 183_notes:examples:netforce [2014/07/10 16:58] – caballero
+++ 183_notes:examples:netforce [2017/12/05 02:48] (current) – pwirving
@@ Line 2: / Line 2: @@
 ====== 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.
+The fan cart is observed to experience a net force to the right.
+Determine the (vector) net force acting on the fan cart.
 ==== Setup ====
@@ Line 16: / Line 17: @@
     * the force applied by the track (directly upward)
     * a frictional forces and air resistance that resist the motion
+  * The acceleration due to gravity is 9.8  $\dfrac{m}{s^2}$  and is directed downward.
 === Lacking ===
-  * The mass of the fan cart is not given, but can be [[http://lmgtfy.com/?q=mass+of+a+pasco+fan+cart|found online]] ($m_{car} = 0.3 kg$).
+  * The mass of the fan cart is not given, but can be [[http://lmgtfy.com/?q=mass+of+a+pasco+fan+cart|found online]] ($m_{cart} = 0.3 kg$).
   * 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  $F_{air} = 0.45 N$ .
@@ Line 35: / Line 37: @@
 ==== Solution ====
-We simply compute the momentum vector.
+We simply compute the force vector noting that the momentum does not change in the vertical direction, so the forces on the cart due to gravity and the force on the cart due to the track are equal in magnitude.
-$$\vec{p}_{car} = m_{car} \vec{v}_{car} = (884.05 kg) \langle 22.35, 0, 1.06\rangle\dfrac{m}{s} = \langle 1.98 \times 10^4, 0, 9.37 \times 10^2\rangle \dfrac{kg\:m}{s}$$
+The force on the cart due to the Earth is given by $F_{Earth} = m\vec{g}$ where $\vec{g} = \langle 0, -9.8, 0 \rangle \dfrac{m}{s^2}$. We compute,
+$$F_{Earth} = m_{cart}\vec{g} = 0.3 kg\:\langle 0, -9.8, 0 \rangle \dfrac{m}{s^2} = \langle 0, -2.94, 0 \rangle N$$
+So, we can now compute the net force,
+$$\vec{F}_{net} = \sum \vec{F}_i  = \vec{F}_{fan} + \vec{F}_{Earth} + \vec{F}_{track} = \langle 0.45, 0, 0 \rangle N + \langle 0, -2.94, 0 \rangle + \langle 0, 2.94, 0 \rangle = \langle 0.45, 0, 0 \rangle N$$
+Notice this is simply the force that the air exerts on the blades. This is the force responsible for the momentum change of the fan cart.