A pulley system of 4 pulleys is used to raise a loan of mass 50kg vertically,if its effeciency is 80%,determine the minimum effort required to raise the load(g=10ms-2)?
see other post.
effort=1/.8 * 50*9.8*k
what is k? that is the mechanical advantage, it will depend on how the pulleys are connected. In this case, the k probably equals 5, but one would have to look at it. https://www.khanacademy.org/science/physics/work-and-energy/mechanical-advantage/v/mechanical-advantage-part-3
To determine the minimum effort required to raise the load using the pulley system, we need to consider the efficiency of the system.
Efficiency is defined as the ratio of output work to input work. In this case, the output work is the work done against gravity to raise the load, and the input work is the work done by the effort force.
The efficiency formula is given by:
Efficiency = (output work / input work) * 100
In this case, the efficiency is given as 80%. So, we can rewrite the formula as:
0.8 = (output work / input work)
Since the output work is the work done against gravity to raise the load, we can calculate it using the formula:
Output work = mass * gravity * height
Given:
Mass (m) = 50 kg
Gravity (g) = 10 m/s^2
Let's assume the height raised by the load is 'h' meters. Then, the output work becomes:
Output work = 50 kg * 10 m/s^2 * h
Now, let's find the input work. In this case, the input work is the work done by the effort force, which is the force applied multiplied by the distance over which the force is applied. Since the pulley system reduces the force required, the input distance is greater than the output distance.
Let's assume that the input distance is 'd' meters and the output distance is 'h' meters.
Input work = effort force * input distance
To determine the minimum effort required, we need to consider the case where the input and output work are equal, and the efficiency is at its maximum (80%).
So, we have:
Input work = Output work
(effort force * d) = (50 kg * 10 m/s^2 * h)
Simplifying, we find:
effort force = (50 kg * 10 m/s^2 * h) / d
Therefore, the minimum effort force required to raise the load is given by the equation:
Effort force = (50 kg * 10 m/s^2 * h) / d
To determine the minimum effort required to raise the load using the given pulley system, you need to consider the efficiency of the pulley system.
Efficiency (η) is defined as the ratio of output work (Wout) to input work (Win) of a machine, expressed as a percentage. It is given by the formula:
η = (Wout / Win) × 100
In this case, the efficiency of the pulley system is given as 80%, or 0.80 in decimal form. We can use this information to find the output work.
Output work (Wout) is the work done by the pulley system to raise the load. It is equal to the product of the load (Wload) and the vertical distance lifted (d).
Wout = Wload × d
To find the load (Wload), we need to consider the weight of the object. The weight of an object is given by the formula:
Wload = mass × gravitational acceleration
In this case, the mass of the load is given as 50 kg, and the acceleration due to gravity (g) is 10 m/s^2. Therefore:
Wload = 50 kg × 10 m/s^2 = 500 N
Now, let's determine the vertical distance lifted (d). Since the load is lifted vertically, the distance lifted is equal to the height (h) at which the load is raised.
Now, let's consider the pulley system. With 4 pulleys, the mechanical advantage (MA) is given by:
MA = 2^(number of pulleys)
In this case, with 4 pulleys, the mechanical advantage is:
MA = 2^4 = 16
The input work (Win) is equal to the effort (E) multiplied by the distance over which the effort is applied (D).
Win = E × D
Since the mechanical advantage is defined as the ratio of output force (Fout) to input force (Fin), we have:
MA = Fout / Fin
Simplifying, we find:
Fin = Fout / MA
Since the effort (E) is equal to the input force (Fin) multiplied by the distance over which the effort is applied (D):
E = Fin × D = Fout / MA × D
Now, let's calculate the minimum effort required using the given values:
E = Fout / MA × D
In this case, the mechanical advantage (MA) is 16. The distance over which the effort is applied (D) is equal to the height (h) at which the load is raised.
Given the factors mass = 50kg, g = 10m/s^2, efficiency = 80%, and the number of pulleys = 4, you can substitute these values into the formulas and calculate the minimum effort required to raise the load.