A worker pushed a 34.0-kg block 10.0 m along a level floor at a constant speed with a force directed 39.0° below the horizontal. If the coefficient of kinetic friction is 0.20, how much work did the worker do on the block?
To calculate the work done by the worker on the block, we need to determine the force applied by the worker and then calculate the work done by this force.
1. First, let's determine the horizontal component of the force applied by the worker. We can do this by finding the cosine of the angle between the force and the horizontal direction:
horizontal component = force * cos(angle)
horizontal component = F * cos(39.0°)
2. Next, we can calculate the frictional force acting on the block. The frictional force is given by the equation:
frictional force = coefficient of friction * normal force
The normal force is equal to the weight of the block, which can be calculated as:
weight = mass * acceleration due to gravity
weight = 34.0 kg * 9.8 m/s^2
Therefore, the frictional force is given by:
frictional force = coefficient of friction * weight
3. Since the block is moving at a constant speed, the force applied by the worker must be equal to the frictional force. Therefore, we can equate the horizontal component of the force applied by the worker with the frictional force:
horizontal component = frictional force
4. Finally, we can calculate the work done by the worker by multiplying the distance the block is pushed by the horizontal component of the force:
work done = horizontal component * distance
Substitute the value of the horizontal component calculated in step 1, and the distance given in the problem (10.0 m), to get the final answer.
Note: Make sure to use consistent units throughout the calculations. Gravity is generally approximated as 9.8 m/s^2, but this value may differ depending on the context.