A 3.01 kg block slides down a frictionless plane inclined 18.6° to the horizontal. If the length of the plane's surface is 1.47 m, how much work is done, and by what force?

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To find the work done on the block as it slides down the inclined plane, we can use the formula:

Work = Force × Distance × cos(θ)

Where:
- Work is the amount of work done (in joules, J)
- Force is the force applied (in newtons, N)
- Distance is the distance moved by the object (in meters, m)
- θ (theta) is the angle between the force and the direction of motion (in degrees)

Given:
- The mass of the block is 3.01 kg.
- The angle of inclination of the plane is 18.6°.
- The length of the surface of the plane is 1.47 m.

Now, let's break down the problem into its components:

1. Find the force applied on the block:
Since the plane is frictionless, the only force acting on the block is its weight, which can be calculated using the formula:
Force = mass × gravity

where the acceleration due to gravity, g, is approximately 9.8 m/s².

So, Force = 3.01 kg × 9.8 m/s².

2. Calculate the distance moved by the block:
The distance moved by the block is the length of the surface of the plane, which is given as 1.47 m.

3. Calculate the angle θ in radians:
To use the cosine function in the formula, we need to convert the angle from degrees to radians.
θ (radians) = θ (degrees) × (π/180)

Substituting the given values, θ (radians) = 18.6° × (π/180).

4. Substitute the values into the work formula:
Work = Force × Distance × cos(θ)

Substitute the calculated values for force, distance, and θ (in radians) into the formula to find the work done by the block.

After performing the calculations, you will find the work done on the block and the force applied.