A block of mass 2.50 kg is pushed 2.40 m along a frictionless horizontal table by a constant 14.0 N force directed 25.0° below the horizontal.
(a) Determine the work done by the applied force.
1 J
(b) Determine the work done by the normal force exerted by the table.
(a) 14.0 cos 25 * 2.40 m = ___ Joules
(b) zero. It is perpendicular to the motion
To determine the work done by the applied force and the work done by the normal force, we need to use the formulas for work.
(a) The work done by a force can be calculated using the formula: work = force × distance × cos(angle)
In this case, the applied force is 14.0 N and it is directed 25.0° below the horizontal. The distance the block is pushed is 2.40 m. Plugging these values into the formula:
work = 14.0 N × 2.40 m × cos(25.0°)
To calculate cos(25.0°), we use a scientific calculator or look it up in a trigonometric table. The value of cos(25.0°) is approximately 0.9063.
work ≈ 14.0 N × 2.40 m × 0.9063
work ≈ 30.854 J
Therefore, the work done by the applied force is approximately 30.854 Joules (J).
(b) The normal force exerted by the table does not do any work in this case because it is perpendicular to the direction of motion. When a force is perpendicular to the displacement, the work done is zero. Hence, the work done by the normal force is 0 J.
Therefore, the work done by the normal force exerted by the table is 0 Joules (J).