A 180 kg block is pulled at a constant speed of 8.3 m/s across a horizontal floor by an applied force of 135 N directed 15° above the horizontal. What is the rate at which the force does work on the block?
To find the rate at which the force does work on the block, we can use the formula:
Work = force * displacement * cos(theta)
Where:
- Work is the amount of work done (in joules),
- force is the applied force (in newtons),
- displacement is the distance the force is applied over (in meters),
- theta is the angle between the force and the direction of displacement (in degrees).
In this case, we are given the applied force (135 N), the speed of the block (8.3 m/s), and the angle above the horizontal (15°).
First, we need to find the displacement. Since the block is moving at a constant speed, the displacement is equal to the distance traveled. We can find the distance traveled using the formula:
distance = speed * time
However, we are not given the time. To find it, we can use the formula:
time = distance / speed
Since the block is moving at a constant speed, the time can be calculated as:
time = displacement / speed
Now, we need to find the displacement. We can use the formula:
displacement = distance * cos(theta)
where distance is the speed * time. We already have the values for speed and theta, so we can plug them into the formula:
displacement = (speed * time) * cos(theta)
Next, we can substitute the values into the formula for work:
Work = force * displacement * cos(theta)
Substituting the given values:
Work = 135 * [(8.3 * displacement/speed)] * cos(15°)
Now, we can simplify and calculate the work:
Work = 135 * (8.3 * displacement/speed) * cos(15°)
Finally, we compute the value:
Work = 135 * (8.3 * displacement/speed) * cos(15°)
Therefore, the rate at which the force does work on the block is equal to the calculated value.