Part A
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?
Solution
System:
Interactions:
Model:
Approach:
Diagrammatic Representation
Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:
Mathematical Representation
Using the free body diagram, we can write the relevant x-component of Newton's 2nd Law:
\begin
[ \sum F_
= F\cos\theta = ma_
] \end
Solving for F:
\begin
[ F = \frac{ma_{x}}
= \mbox
]\end
Part B
A person pulls a box of mass 15 kg along a smooth floor by applying a force F at an angle of 30° above the horizontal.. The box accelerates horizontally at a rate of 2.0 m/s2. What is the magnitude of F?
Solution
System:
Interactions:
Model:
Approach:
Diagrammatic Representation
Before writing Newton's 2nd Law for the x direction, we choose coordinates and break the applied force F into x- and y-components:
Mathematical Representation
The free body diagram implies:
\begin
[ \sum F_
= F\cos\theta = ma_
] \end
Solving for F:
\begin
[ F = \frac{ma_{x}}
= \mbox
]\end