A crate of mass 20kg was moved up a rough plane inclined at 30degree to the ground. If the crate was moved a distance of 5m after 10mins. Determine the total rate at work done.
ANSWER
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To determine the total rate at which work is done, we need to calculate the work done against gravity and the work done against friction on the rough plane.
First, let's calculate the work done against gravity. The work done against gravity is given by the equation:
Work = force x distance x cos(angle)
In this case, the force is the weight of the crate, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). The distance is the vertical distance moved, which can be calculated using the formula:
Vertical distance = distance x sin(angle)
Substituting the given values:
Mass of the crate = 20 kg
Distance = 5 m
Angle = 30 degrees
Vertical distance = 5 m x sin(30 degrees) = 5 m x 0.5 = 2.5 m
Now, we can calculate the work done against gravity:
Work against gravity = (mass x acceleration due to gravity) x vertical distance x cos(angle)
Work against gravity = (20 kg x 9.8 m/s^2) x 2.5 m x cos(30 degrees)
Next, let's calculate the work done against friction on the rough plane. The work done against friction can be calculated using the formula:
Work against friction = force of friction x distance
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction x normal force
The normal force can be calculated using the formula:
Normal force = mass x gravity x cos(angle)
Substituting the given values:
Mass of the crate = 20 kg
Angle = 30 degrees
Normal force = 20 kg x 9.8 m/s^2 x cos(30 degrees)
Then, we need to calculate the coefficient of friction, which is not given in the question. You will need to find this value from the question or other available sources.
Once you have the coefficient of friction, you can calculate the force of friction, and then the work done against friction using the given distance.
Finally, to determine the total rate at which work is done, we can divide the total work done by the time taken:
Total work done = Work against gravity + Work against friction
Total rate of work done = Total work done / Time
Please note that you will need to substitute the appropriate values into the equations to calculate the specific values.