A hardworking ant must supply 0.00955 N to pull a small piece of fruit at constant velocity over a distance of 8.60 cm up a small hill to the entrance of the colony. If the coefficient of kinetic friction between the piece of fruit and the 16.2° sloped hill is 0.540, calculate the work done by the ant by pulling the piece of fruit up the hill.

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To calculate the work done by the ant in pulling the piece of fruit up the hill, we need to consider the following steps:

Step 1: Calculate the force of friction
The force of friction can be calculated using the formula:

Force of friction (f) = μ * Normal force

where μ is the coefficient of kinetic friction and the normal force is the perpendicular force exerted by the slope on the fruit.

The normal force can be calculated using the formula:

Normal force = mass * gravitational acceleration * cos(θ)

where mass is the mass of the fruit and gravitational acceleration is the acceleration due to gravity (9.8 m/s^2). θ is the angle of the slope (16.2° in this case).

Step 2: Calculate the distance
The distance over which the ant pulls the fruit is given as 8.60 cm, which can be converted to meters by dividing by 100.

Step 3: Calculate the work done
The work done can be calculated using the formula:

Work = force * distance

where force is the force exerted by the ant and distance is the distance over which the force is applied.

Now, let's calculate the work done by the ant.

Step 1: Calculate the force of friction
Normal force = mass * gravitational acceleration * cos(θ)
Normal force = 0.00955 kg * 9.8 m/s^2 * cos(16.2°)

Step 2: Calculate the distance
Distance = 8.60 cm ÷ 100 = 0.0860 m

Step 3: Calculate the work done
Work = force * distance
Work = (μ * Normal force) * distance

Plug in the values and calculate the work.