an off-road dumper truck can hold 325 tons of gravel. how much work must be done on the gravel to raise it an average of 9.2 m to get it into the truck
Well, one thing is for sure - that truck must really have strong tires to handle all that weight! As for the work needed to raise the gravel, let me calculate it for you...
To calculate the work done, we need to multiply the force required by the distance over which it is applied. In this case, the force required is the weight of the gravel, which we can find using the formula:
Force = mass x gravitational acceleration
Since the truck can hold 325 tons of gravel, which is equivalent to 325,000 kilograms, and the gravitational acceleration is approximately 9.8 m/s², we can calculate the force:
Force = 325,000 kg x 9.8 m/s²
Now, we need to calculate the distance over which the work is done, which is given as an average of 9.2 meters.
Finally, we can calculate the work done using the formula:
Work = Force x Distance
Plug in the values and let the calculation begin... Voila!
Work = (325,000 kg x 9.8 m/s²) x 9.2 m
But, hey, why do all those calculations when we can just let the truck do the heavy lifting? It'll handle all the work for you while you sit back and enjoy the show!
To calculate the work required to raise the gravel, we need to consider the weight of the gravel and the height it needs to be raised.
Given:
- Weight of gravel = 325 tons
- Average height to raise = 9.2 m
We can use the formula for work (W) which is equal to the force (F) multiplied by the distance (d) moved in the direction of the force.
1. Convert the weight of the gravel from tons to kilograms:
1 ton = 1000 kg
325 tons = 325 * 1000 kg = 325,000 kg
2. Calculate the force required:
F = m * g
where m is the mass of the gravel and g is the acceleration due to gravity, approximately 9.8 m/s².
F = 325,000 kg * 9.8 m/s² = 3,185,000 N
3. Calculate the work done:
W = F * d
W = 3,185,000 N * 9.2 m = 29,288,200 J (Joules)
Therefore, approximately 29,288,200 Joules of work needs to be done to raise the gravel an average of 9.2 meters and get it into the truck.
To determine the amount of work required to raise the gravel, we need to use the formula:
Work = Force * Distance
In this case, the force is equal to the weight of the gravel, and the distance is the height it needs to be raised.
First, let's convert the weight of the gravel from tons to kilograms, as it is a more commonly used unit for force calculations.
1 ton = 1000 kilograms
So, the weight of the gravel in kilograms is:
325 tons * 1000 kilograms/ton = 325,000 kilograms
Now, let's convert the height from meters to centimeters, as it is a more commonly used unit for force calculations.
1 meter = 100 centimeters
So, the height to be raised in centimeters is:
9.2 meters * 100 centimeters/meter = 920 centimeters
Now that we have the weight of the gravel and the height to be raised, we can calculate the work:
Work = Force * Distance
Work = 325,000 kilograms * 920 centimeters
Work = 299,000,000 kilogram-centimeters
The work required to raise the gravel an average of 9.2 meters into the truck is 299,000,000 kilogram-centimeters.