a cart accelerates from rest along a level track as a result of the action of a fan. (a) Since the cart accelerates then according to Newton’s Second Law there must be a net horizontal force on it. What is the source of that force? Hints: (1)The fan cart unit cannot exert a force on itself, (2) What does Newton’s Third Law tell you?, (3) Would the fan cart unit accelerate if it were in outer space? (b) If friction is negligible identify the three forces acting on the cart and describe the direction of there forces relative the the coordinate system shown when the movie is opened in VideoPoint. (c)find the magnitude and direction of the acceleration of the cart in the horizontal direction. Explain how you determined the acceleration. Is it constant? How do you know? (d) What is the net work done on the cart as it travels from its location in frame 1 to its location in frame 14? What agent does this work?
a) The source of the force that is making the cart accelerating is the fan itself. The mechanism of the force is the following: the fan blows air in a direction opposing the motion of the cart. This way the mass of air blown which initially had zero momentum, is given a certain momentum backwards. Since the total momentum of the blown air and cart needs to be the same, the cart will acquire a momentum forward. Since the momentum of the cart has a variation, this is in turn equivalent to a pushing force acting on the cart. Since in outer space air does not exist the cart would not accelerate if situated in vacuum.
b) The figure is attached below. On a free body diagram, the three forces acting on the cart are its weight downwards `G` , the pushing force of the fan `F` and the reaction from the ground that sustains the cart on the track `N` . The fourth force that is not shown usually on the free body diagram is the cart inertia itself `m*a` .
By writing all forces as vectors the second principle of physics is
G+ F+N= m*a
Since on the vertical axis we have `G=N` then on the horizontal axis it remains
`F =m*a rArr a =F/m`
The acceleration has the same direction as the pushing force of the fan acting on the cart, forward. As long as the force of the fan is the same along the entire motion the acceleration is constant.
d) To determine the work, one needs to know the total displacement of the cart between the starting and ending points. Since the weight of the cart `G` is equilibrating the ground reaction `N` it remains only the pushing force of the fan `F` to do this work.