A 11.5 m long conveyor belt, inclined at 30.0°, is used to transport bundles of newspapers from the mailroom up to the cargo bay to be loaded on to delivery trucks. Each newspaper has a mass of 1.0 kg, and there are 21 newspapers per bundle. Determine the power that the conveyor develops if it delivers 15 bundles per minute.
How far do we lift this?
11.5 sin 30 = 5.75
mass of a bundle = 1 * 21 = 21 kg
increase of potential energy of bundle = m g h = 21 * 9.8 * 5.75 = 1183 Joules
so we do 1183 Joules * 15 lifts in 60 seconds = 296 watts
Now it is not clear to me from the question if the newspapers are already moving when they hit the belt (like from a horizontal belt) If not, they must also be given kinetic energy by the belt.
Therefore that is the best I can do for you.
It's the best that I need. I appreciate the help! :)
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To determine the power that the conveyor belt develops, we need to calculate the work done per unit time (power).
The work done by the conveyor belt can be calculated by multiplying the force exerted by the belt (the weight of the newspapers) by the distance it moves in a given time.
Step 1: Calculate the weight of a single bundle of newspapers.
The weight of a single newspaper can be calculated using the formula:
Weight = mass * gravity
where mass is the mass of a single newspaper and gravity is the acceleration due to gravity (9.8 m/s^2).
Mass of a single newspaper = 1.0 kg
Gravity = 9.8 m/s^2
Weight of a single newspaper = 1.0 kg * 9.8 m/s^2
Step 2: Calculate the weight of a bundle of newspapers.
Since there are 21 newspapers per bundle, we can multiply the weight of a single newspaper by 21 to get the weight of a single bundle.
Weight of a bundle of newspapers = Weight of a single newspaper * 21
Step 3: Calculate the work done by the conveyor belt per bundle.
The work done by the conveyor belt is given by the formula:
Work = Force * Distance
Since the bundle of newspapers is being moved up an inclined plane, we need to consider the component of the weight along the direction of the conveyor belt.
Force = Weight of a bundle * sin(theta)
where theta is the angle of inclination (30.0 degrees).
Work done per bundle = Force * distance
where distance is the length of the conveyor belt (11.5 m).
Step 4: Calculate the work done per unit time (power).
Since the conveyor belt delivers 15 bundles per minute, we can divide the work done per bundle by the time taken to move one bundle.
Power = Work done per bundle / Time taken for one bundle
Now we can substitute the calculated values into the formulas and calculate the power developed by the conveyor belt.