A force of 2000N is used to push a box up am inclined plane that is 15m long. If the 100 kg box is raised to a height of 8m,how much work is done against friction ?let g=10m/s^2.
To find the work done against friction, we first need to calculate the work done to lift the box to a height of 8m.
The work done to lift an object is given by the formula: Work = force * distance * cos(theta), where theta is the angle between the force and the direction of motion.
In this case, the force used to lift the box is equal to the weight of the box, which is given by the formula: weight = mass * gravity.
So, weight = 100 kg * 10 m/s^2 = 1000N.
The angle between the force and the direction of motion is the angle of the inclined plane, which we can find using trigonometry. The angle is given by the formula: angle = arctan(height/distance).
So, angle = arctan(8m/15m) = 29.53 degrees.
Now, let's calculate the work done to lift the box to a height of 8m:
Work = force * distance * cos(theta)
= 1000N * 15m * cos(29.53 degrees)
= 12990 J (rounded to the nearest whole number).
Next, we need to calculate the total work done by the applied force against gravity. The work against gravity is equal to the decrease in potential energy.
Potential energy = mass * gravity * height
= 100 kg * 10 m/s^2 * 8m
= 8000 J.
Therefore, the work done against friction is the difference between the total work done (work done to lift the box plus work done against gravity) and the work done to lift the box:
Work against friction = Total work - Work to lift the box
= (8000 J + 12990 J) - 12990 J
= 8000 J.
Thus, the work done against friction is 8000 Joules.