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:

    Box as point particle.

    Interactions:

    External influences from the person (applied force) the earth (gravity) and the floor (normal force).

    Model:

    Point Particle Dynamics.

    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:

    Solving for F:

    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:

    Box as point particle.

    Interactions:

    External influences from the person (applied force) the earth (gravity) and the floor (normal force).

    Model:

    Point Particle Dynamics.

    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:

    Solving for F: