Answer :
The work done by the force of gravity in joules is approximately 245 J. The closest answer is option a. 245.
To find the work done by the force of gravity as the block slides down the incline, we can use the formula:
Work = Force * Distance * cos(theta),
where:
Force is the component of the force of gravity parallel to the incline,
Distance is the length of the incline, and
theta is the angle of inclination of the incline.
In this case, the force of gravity can be decomposed into two components: one perpendicular to the incline (mg * cos(theta)) and one parallel to the incline (mg * sin(theta)). Since the block is sliding down the incline, the force of gravity parallel to the incline is the one that does the work.
Given:
Mass of the block (m) = 5.0 kg,
Inclination angle (theta) = 30 degrees, and
Length of the incline (distance) = 10 m,
First, let's find the component of the gravitational force acting parallel to the incline:
F_ parallel = m * g * sin(theta)
where m = 5.0 kg (mass of the block), g = 9.81 m/s² (acceleration due to gravity), and theta = 30° (angle of inclination).
F_ parallel = 5.0 kg * 9.81 m/s² * sin(30°) = 24.525 N
Now, let's calculate the work done by the force of gravity:
Work = F_ parallel * distance
where distance = 10 m (length of the incline).
Work = 24.525 N * 10 m = 245.25 J
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