While a roofer is working on a roof that slants at 45.0 degrees above the horizontal, he accidentally nudges his 94.0 N toolbox, causing it to start sliding downward, starting from rest.
Incomplete.
To determine the motion of the toolbox as it slides downward, we can analyze the forces acting on it.
First, let's consider the forces in the horizontal direction. Since the roof is slanted at 45.0 degrees above the horizontal, the effective force of gravity acting in the horizontal direction can be calculated by multiplying the toolbox's weight by the sine of the angle:
Horizontal force = weight of toolbox × sin(angle)
The weight of the toolbox is given as 94.0 N, so the horizontal force is:
Horizontal force = 94.0 N × sin(45.0 degrees) = 66.5 N
Next, let's consider the forces in the vertical direction. The force of gravity acting vertically downward can be calculated by multiplying the toolbox's weight by the cosine of the angle:
Vertical force = weight of toolbox × cos(angle)
Substituting the given values:
Vertical force = 94.0 N × cos(45.0 degrees) = 66.5 N
Since there is no external horizontal force acting on the toolbox, the horizontal force of 66.5 N will cause the toolbox to slide downward along the roof. The vertical force of 66.5 N counteracts the downward force of gravity, resulting in the toolbox sliding downward with a constant velocity.
Therefore, the toolbox will slide downward along the roof, but it will not accelerate or decelerate.