Physics & Astronomy
The work done by a constant force is equal to the product of the magnitude of the displacement and the component of the force parallel to the displacement.
is the constant force,
is the displacement, and
is the angle between the force and the displacement.
If the force or force component acts in the same direction of the displacement, then the work is said to be positive. If the force or force component acts in the opposite direction of the displacement, then the work is said to be negative.
When the catcher catches the fastball, the force will act in the opposite direction of the displacement to stop the fastball. Hence, the work is said to negative.
Therefore, the options (a) and (c) are wrong and the correct option is (b).
The work done
When we go straight up, the gravitational force makes an angle 180 0 with the displacement. But, if we go in zigzag path it makes less angle with gravitational force. That is why it is easier to go up in a zigzag path than straight.
Work done is defined as the dot product of force and displacement
Here, F is the force vector and s is the displacement and
is the angle between them.
Consider the following diagram
The only force acting along the motion of block is
is the angle of inclination. Hence this is the only force responsible for the work done.
Angle between the motion and force vector is
Thus, work done by this force is,
Substitute 3 kg for m , 1.5 m for s, 9.8
Hence, the work done is
which is done by component of its weight.