a 65 kg object is pulled at a constant velocity up an incline w/ a force of 95 N parallel to the incline. Assuming that the difference between the work output and input is work required to overcome friction, what is the force of friction along the incline (the length of the incline is 5 m, the height is 1.92 m and the efficiency of this machine is 68.2%).
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To find the force of friction along the incline, we first need to calculate the work done to pull the object up the incline and the work input.
First, let's calculate the work done to lift the object to its final height. The work done against gravity is given by the formula:
Work = force * distance * cos(angle)
The force required to lift the object against gravity can be calculated using the mass of the object (65 kg) and the acceleration due to gravity (9.8 m/s^2):
Force_gravity = mass * gravity
Now we can substitute the given values into the formula:
Force_gravity = 65 kg * 9.8 m/s^2
Next, we need to calculate the distance traveled along the incline using the length and height of the incline. The distance traveled along the incline can be calculated using the Pythagorean theorem:
Distance = sqrt(length^2 + height^2)
Now, let's calculate the work done to lift the object:
Work_done = Force_gravity * Distance * cos(angle)
Next, we need to calculate the work input. The work input is the force applied to pull the object parallel to the incline multiplied by the distance traveled along the incline:
Work_input = Force_input * Distance
Now, we can calculate the work required to overcome friction as the difference between the work input and work output:
Work_friction = Work_input - Work_done
Finally, we can calculate the force of friction using the equation:
Force_friction = Work_friction / Distance
The efficiency of the machine is given as 68.2%. Efficiency is defined as the ratio of useful work output to work input:
Efficiency = Work_done / Work_input
We can rearrange this equation to solve for Work_done:
Work_done = Efficiency * Work_input
Now, substitute this back into the equation for Work_friction and solve for Force_friction:
Force_friction = (Work_input - (Efficiency * Work_input)) / Distance
Substitute the given values for the force of 95 N, the length of the incline of 5 m, the height of 1.92 m, and the efficiency of 68.2% into the equation to find the force of friction.