Part A
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A person pushes a box of mass 15 kg along a smooth floor by applying a force F at an angle of 30° below the horizontal.. The box accelerates horizontally at a rate of 2.0 m/s2. What is the magnitude of F?
System: Box as point particle subject to external influences from the person (applied force) the earth (gravity) and the floor (normal force).
Model: Point Particle Dynamics.
Approach: Before writing Newton's 2nd Law for the x direction, we break the applied force F into x- and y-components:
This implies:
\begin
[ \sum F_
= F\cos\theta = ma_
] \end
Solving for F:
\begin
[ F = \frac{ma_{x}}
] = \mbox
]\end
Part B
A person pushes a box of mass 15 kg along a smooth floor by applying a perfectly horizontal force F. The box moves horizontally at a constant speed of 2.0 m/s in the direction of the person's applied force. What is the magnitude of F?
System and Model: As in Part A.
Approach: Just as above, Newton's 2nd Law for the x direction can be written:
\begin
[ \sum F_
= F = ma_
] \end
This time, however, the acceleration requires some thought. The speed of the box and its direction of motion are constant. Thus, by definition, the acceleration is zero. This implies:
\begin
[ F = ma_
= \mbox
^
) = \mbox
] \end
This result is probably not consistent with your everyday experience. The reason for this is that it is very difficult to find a box and floor combination with zero friction. Instead, consider the effort that would be required to keep an air-hockey puck moving at constant speed on the air-table (friction is very small) or to keep a soccer ball rolling at constant speed on a smooth, level floor (friction is unimportant since the ball is rolling).