An inclined plane, which slopes at 37 o, is used to raise a 10kg object to a height of 4m. If the efficiency of this machine is 80%. The amount of the load force will be _____
To find the load force, we first need to find the effort force.
The efficiency of the machine is given by the formula:
Efficiency = (load force / effort force) * 100
Since the efficiency is 80%, we can write the equation as:
80 = (load force / effort force) * 100
Simplifying the equation, we get:
0.8 = load force / effort force
Rearranging the equation, we find:
effort force = load force / 0.8
Now, let's find the effort force.
The inclined plane raises the object to a height of 4m. The work done by the effort force is given by:
Work = force * distance
The distance is the height, which is 4m. The force is the effort force, and we want to find this value.
The work done by the effort force is equal to the potential energy gained by the object.
Potential energy = m * g * h
where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height (4m).
Potential energy = 10 * 9.8 * 4 = 392 J
Now, we can solve for the effort force:
392 = effort force * 4
effort force = 392 / 4 = 98 N
Using the equation for efficiency, we can find the load force:
0.8 = load force / 98
load force = 0.8 * 98 = 78.4 N
Therefore, the amount of the load force will be 78.4 N.
To find the amount of the load force, we first need to determine the input work and the output work of the machine.
The work done on the inclined plane (input work) is given by the equation:
Work input = force input * distance
Since the inclined plane is used to raise the object, the force input is equal to the weight of the object.
Force input = m * g
where m is the mass of the object (10kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Force input = 10kg * 9.8 m/s^2
= 98 N
The distance is given as 4m.
Work input = 98 N * 4m
= 392 J
The output work is the work done against gravity, which is equal to the weight of the object multiplied by the vertical distance it is raised.
Work output = force output * distance
The force output is equal to the load force.
Work output = load force * distance
The distance is given as 4m.
Work output = load force * 4m
We know that the machine's efficiency is 80%. The efficiency of a machine is given by the equation:
Efficiency = (work output / work input) * 100
Substituting in the given values, we can solve for the load force.
80% = (work output / 392 J) * 100
Dividing both sides by 100:
0.8 = (work output / 392 J)
Multiplying both sides by 392 J:
work output = 0.8 * 392 J
= 313.6 J
Now we can substitute this value back into the equation for work output:
313.6 J = load force * 4m
Dividing both sides by 4m:
load force = 313.6 J / 4m
= 78.4 N
Therefore, the amount of the load force will be 78.4 N.