the efficiency of a machine is 80% determine the work done by a person using this machine to raise a load of 200kg through a vertical distance of 3.0m {take g=10m/s}
pls help.me
what is 200*g*3/.80 ?
To find the work done by a person using the machine, we need to first calculate the work done on the load.
The work done on an object is given by the equation:
Work = Force x Distance x cos(angle)
In this case, the force required to raise the load is equal to its weight, which can be calculated using the equation:
Force = mass x gravity
Given:
Mass of the load (m) = 200 kg
Vertical distance (h) = 3.0 m
Acceleration due to gravity (g) = 10 m/s²
Calculating the force:
Force = mass x gravity
Force = 200 kg x 10 m/s²
Force = 2000 N
Using the equation for work:
Work = Force x Distance x cos(angle)
In this case, the work is done vertically upwards, so the angle between the force and the direction of motion is 0°, and cos(0°) = 1.
Substituting the values:
Work = 2000 N x 3.0 m x 1
Work = 6000 Nm
Now, to find the work done by the person using the machine, we need to consider the efficiency of the machine. The efficiency of a machine is given by the equation:
Efficiency = (Useful output energy / Input energy) x 100%
In this case, the useful output energy is equal to the work done on the load, and the input energy is the work done by the person using the machine.
Let W_person be the work done by the person.
Efficiency = (Work done on the load / Work done by the person) x 100%
Given: Efficiency = 80%
Substituting the known values, we can solve for W_person:
80% = (6000 Nm / W_person) x 100%
80% = 6000 Nm / W_person
W_person = 6000 Nm / 80%
W_person = 6000 Nm / 0.8
W_person = 7500 Nm
Therefore, the work done by the person using the machine to raise the load is 7500 Nm.
To determine the work done by a person using the machine, we first need to calculate the input work and then multiply it by the efficiency of the machine.
The input work is the work done by the person, which can be calculated using the formula:
Input work = Force x Distance
In this case, the force is equal to the weight of the load, which can be calculated as:
Force = mass x acceleration due to gravity
Since the load is being raised vertically, the acceleration due to gravity can be taken as g = 10m/s². Therefore:
Force = 200kg x 10m/s²
Now, let's calculate the force:
Force = 200kg x 10m/s² = 2000N
Next, we need to calculate the distance. The distance is given as 3.0m.
Now, we can calculate the input work:
Input work = Force x Distance = 2000N x 3.0m = 6000Nm
Finally, to determine the work done by a person using this machine, we need to multiply the input work by the machine's efficiency.
The efficiency of the machine is given as 80%, which can be written as 0.8.
Work done by person = Input work x Efficiency
= 6000Nm x 0.8
= 4800Nm
Therefore, the work done by a person using this machine to raise a load of 200kg through a vertical distance of 3.0m is 4800Nm.