The spiral shaft in a grain auger raises grain from a farmers truck into a storage bin. Assume that the auger does 6.2 x 10*5 J of work on a certain amount of grain to raise it 4.2 m from the truck to the top of the bin.What is the total mass of the grain moved?
Work = M*g*H, so
M = Work/(g*H)
To find the mass of the grain moved, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done by the grain auger can be calculated using the formula W = Fd, where W is the work done, F is the force applied, and d is the distance moved.
Given that the work done is 6.2 x 10^5 J and the distance moved is 4.2 m, we can rewrite the formula as:
6.2 x 10^5 J = F x 4.2 m
To find the force, we need to know the weight of the grain. The weight is given by the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity (9.8 m/s^2).
Rearranging the formula, we get:
F = W/g
Substituting the known values, we can find the force F:
F = (6.2 x 10^5 J) / (4.2 m) = 1.476 x 10^5 N
Now we can calculate the mass of the grain:
F = mg
Rearranging the formula, we get:
m = F/g
Substituting the known values:
m = (1.476 x 10^5 N) / (9.8 m/s^2) ≈ 1.506 x 10^4 kg
Therefore, the total mass of the grain moved is approximately 1.506 x 10^4 kg.
To find the total mass of the grain moved, we can use the work-energy principle. According to the principle, the work done on an object is equal to its change in potential energy.
The formula for work is given by:
Work = Force × Distance
In this case, the work done by the grain auger can be calculated by multiplying the force exerted by the auger with the distance it raises the grain. The force exerted by the auger is equal to the weight of the grain.
The formula for weight is given by:
Weight = Mass × Acceleration due to gravity
Since the only force acting on the grain is its weight, we can calculate the work done by the auger as:
Work = Weight × Distance
Given that the work done by the auger is 6.2 × 10^5 J and the distance raised is 4.2 m, we can plug these values into the equation:
6.2 × 10^5 J = Weight × 4.2 m
Now, let's solve for the weight:
Weight = (6.2 × 10^5 J) / (4.2 m)
Weight = 1.476 × 10^5 N
Now we can use the weight formula to find the mass of the grain:
Weight = Mass × Acceleration due to gravity
1.476 × 10^5 N = Mass × 9.8 m/s^2
Mass = (1.476 × 10^5 N) / (9.8 m/s^2)
Mass = 1.507 × 10^4 kg
Therefore, the total mass of the grain moved is 1.507 × 10^4 kg.