A block of mass 3.90 kg is pushed 3.80 m along a frictionless horizontal table by a constant 16.0 N force directed 24.0° below the horizontal.
What is th total work done on the block?
16 cos24 N * 3.80 m = 55.5 J
The mass does not matter in the computation of work done, but it does deternmine how fast it accelerates
To find the total work done on the block, we need to calculate the work done by the applied force and the work done by the gravitational force. Let's break down the problem into separate components and calculate each one:
1. Work done by the applied force:
The applied force is 16.0 N and is directed at an angle of 24.0° below the horizontal. Since the displacement and force are not in the same direction, we need to consider the component of the force in the direction of displacement.
The horizontal component of the force can be calculated using the equation:
F_horizontal = F_applied * cos(theta)
F_horizontal = 16.0 N * cos(24.0°)
F_horizontal = 16.0 N * 0.9135
F_horizontal = 14.616 N
Now, we can calculate the work done by the applied force along the horizontal direction:
Work_applied = F_horizontal * displacement
Work_applied = 14.616 N * 3.80 m
Work_applied = 55.66 J
2. Work done by the gravitational force:
The block is moved horizontally, so there is no vertical displacement. Therefore, the work done by the gravitational force is zero because it is perpendicular to the displacement.
Total work done on the block = Work_applied + Work_gravitational
Total work done on the block = 55.66 J + 0 J
Total work done on the block = 55.66 J
Therefore, the total work done on the block is 55.66 J.