Pushing A Vacuum

Pushing a vacuum, though we may not think so, requires a lot of physics. First, the vacuum itself provides an excellent opportunity to draw a free body diagram where all of the forces on the vacuum are

labeled (see diagram).

When pushing a vacuum, you must first apply enough force (which must be compnonentized to find the horizontal component, since you apply force to a vacuum at an angle) to overcome the force of static friction (Fsmax=us(coefficient of static friction) x Fn). This will cause

the vacuum to accelerate forwards as the force of kinetic friction comes into play (kinetic friction opposes the direction of motion of the vacuum). The acceleration of the vacuum can be found using Fnet=ma, F-fk=mass x acceleration, acceleration=(F-fk)/mass.

Also because I am moving the vacuum forward, I am doing work on the vacuum. Work= force x displacement. Because I am applying force at an angle I must componentize the force vector to find the horizontal component of force, so Work=Force(cos(theta)) x Displacement. However, if I were applying force on the vacuum, but it was not moving, even though it may feel as though I am working hard at trying to move the vacuum, I would not be doing any work because their is no displacement of the vacuum. In order for work to occur, their must be both displacement and force.