A block and tackle having a velocity ratio of 5 is used to raise a load of 400N through a distance of 10m. If the work done against friction is 100J. Calculate
1. Efficiency of the machine
2. The effort applied
1. W = F*d = 400*10 = 4,000 J.
e = 4000/(4000+100) = 0.98 = 98 %.
2. e = L/E*Vr
0.98 = 400/5E
E = 82 N.
Can you please explain the answer 2.well for me .
Thank you
I don't understand
1. Efficiency of the machine:
Efficiency is defined as the ratio of output work to input work, expressed as a percentage. The output work is equal to the work done against gravity (Wout), which is the product of the force applied (load) and the distance lifted (Wout = force * distance). The input work (Win) is the sum of the work done against gravity and the work done against friction (Win = Wout + work done against friction).
Given: Load (force) = 400N, Distance lifted = 10m, Work done against friction = 100J.
Wout = force * distance = 400N * 10m = 4000J
Win = Wout + work done against friction = 4000J + 100J = 4100J
Efficiency = (Wout / Win) * 100
= (4000J / 4100J) * 100
≈ 97.56%
Therefore, the efficiency of the machine is approximately 97.56%.
2. The effort applied:
Velocity ratio (VR) is defined as the ratio of the distance the effort (force) moves to the distance the load (resistance) moves. Velocity ratio (VR) = Distance moved by effort / Distance moved by load.
Given: Velocity ratio (VR) = 5, Distance lifted (load) = 10m.
VR = Distance moved by effort / Distance moved by load
5 = Distance moved by effort / 10m
Distance moved by effort = VR * Distance moved by load
Distance moved by effort = 5 * 10m
Distance moved by effort = 50m
Since effort is equal to force multiplied by distance (Effort = force * distance), we can calculate the effort applied as follows:
Force (effort) = Wout / distance moved by effort
Force (effort) = 4000J / 50m
Force (effort) = 80N
Therefore, the effort applied is 80N.
To calculate the efficiency of the machine, we need to determine the work input and the work output.
1. First, let's find the work input.
The work input is the product of the effort applied and the distance it moves.
Work input = Effort * Distance
Given that the load is being raised a distance of 10m, and the work done against friction is 100J, we can calculate the work input as follows:
Work input = Work output + Work done against friction
Work input = Work output + 100J
2. Next, let's find the work output.
The work output is the product of the load being raised and the distance it moves.
Work output = Load * Distance
Given that the load being raised is 400N and the distance is 10m, we can calculate the work output as follows:
Work output = 400N * 10m
Work output = 4000J
Now, we can calculate the efficiency of the machine.
Efficiency = (Work output / Work input) * 100
Using the values we calculated, we have:
Efficiency = (4000J / (Work output + 100J)) * 100
1. Efficiency of the machine:
Efficiency = (4000J / (4000J + 100J)) * 100
Efficiency = (4000J / 4100J) * 100
Efficiency ≈ 97.56%
2. The effort applied:
The effort applied is the amount of work input required to raise the load.
Effort applied = Work input / Distance
Using the values we calculated, we have:
Effort applied = (Work output + 100J) / 10m
Effort applied = (4000J + 100J) / 10m
Effort applied = 4100J / 10m
Effort applied = 410N
Therefore, the efficiency of the machine is approximately 97.56%, and the effort applied is 410N.