a block and tackle system of pulleys consisting of 5 pulleys is used to raise a load of 500N through a height of 12m. if the total work done by the system is 7200j calculate the work done against friction and efficiency of the system
work done on the load ... w = f * d = 500 N * 12 m = 6000 J
work against friction = 7200 J - 6000 J
efficiency = 6000 / 7200
Why did the block and tackle system hire a pulley? Because it didn't want to pull a muscle! Now, let's tackle your question.
To determine the work done against friction, we need to find the work done by the system and subtract the total work done. Since we know the total work done is 7200 J, we can calculate the work done by the system as follows:
Work done by the system = 7200 J
Next, we'll calculate the force (F) required to raise the load. Since the load is lifted through a height of 12 m and the force is given by:
Force (F) = 500 N
Distance (d) = 12 m
Work done by the system = Force × Distance
7200 J = F × 12 m
We can rearrange the formula to find the value of F:
F = 7200 J / 12 m
F = 600 N
So, the force required to raise the load is 600 N.
Now let's calculate the work done against friction. Since work done against friction is equal to force times distance, and we know the force and distance, we can plug those values in:
Work done against friction = F × d
Work done against friction = 600 N × 12 m
Work done against friction = 7200 J
The work done against friction is also 7200 J.
Finally, let's calculate the efficiency of the system. Efficiency is given by:
Efficiency = (Useful output work / Total input work) × 100%
Efficiency = (Work done by the system / Total work done) × 100%
Efficiency = (7200 J / 7200 J) × 100%
Efficiency = 100%
The efficiency of the system is 100%.
So, the work done against friction is 7200 J, and the efficiency of the system is 100%.
To find the work done against friction, we need to first calculate the work done by the system. The work done by the system can be calculated using the formula:
Work = Force x Distance
Given:
Load = 500N
Height = 12m
Total Work = 7200J
We can calculate the force required to lift the load using the formula:
Force = Load/Number of Pulleys
Force = 500N / 5 = 100N
Now, we can calculate the work done by the system:
Work = Force x Distance
7200J = 100N x 12m
Next, we can calculate the work done against friction by subtracting the work done by the system from the total work:
Work against friction = Total Work - Work done by the system
Work against friction = 7200J - (100N x 12m)
Finally, we can calculate the efficiency of the system using the formula:
Efficiency = (Work done by the system / Total Work) x 100
Efficiency = (Work done by the system / (Work done by the system + Work against friction)) x 100
Now, let's calculate the work done against friction and the efficiency of the system:
Work against friction = 7200J - (100N x 12m)
Work against friction = 7200J - 1200J
Work against friction = 6000J
Efficiency = (Work done by the system / (Work done by the system + Work against friction)) x 100
Efficiency = (7200J / (7200J + 6000J)) x 100
Efficiency = (7200J / 13200J) x 100
Efficiency = 0.545 x 100
Efficiency = 54.5%
Therefore, the work done against friction is 6000J and the efficiency of the system is 54.5%.
To calculate the work done against friction and efficiency of the system, we need to make a few assumptions.
Assumptions:
1. The pulleys and ropes are ideal, meaning they have no mass or friction.
2. The efficiency of the system is equal to the mechanical advantage of the block and tackle system.
Given:
- Load force (F) = 500 N
- Height lifted (h) = 12 m
- Total work done (W) = 7200 J
- Number of pulleys (n) = 5
To calculate the work done against friction, we need to find the work done against the load force while neglecting the work done against friction.
Work done against friction (W_friction) = W - Work done against load force
Work done against load force = Force × Distance
1. Calculate the distance lifted by the load:
Distance = height lifted / number of pulleys (h / n)
Distance = 12 m / 5 = 2.4 m
2. Calculate the work done against the load force:
Work done against the load force = Force × Distance
Work done against the load force = 500 N × 2.4 m
Now, we can calculate the work done against friction:
W_friction = W - Work done against the load force
W_friction = 7200 J - (500 N × 2.4 m)
To find the efficiency of the system, we need to calculate the mechanical advantage (MA) of the block and tackle system, given by:
Mechanical Advantage (MA) = Distance moved by effort / Distance moved by load
In this case, Distance moved by effort = Distance moved by load / number of pulleys
Distance moved by effort = 2.4 m / 5
Now, we can calculate the efficiency of the system:
Efficiency (η) = MA (Mechanical Advantage) × 100%
Efficiency (η) = (Distance moved by effort / Distance moved by load) × 100%