A machine with velocity ratio 5 requires 1000J of work o raise a load of 600N through a vertical distance of 1.25m
find i.work output
ii.the efficiency of the machine
iii.the mechanical advantage of the machine
output: 600*1.5 joules
efficience= output/input
MA= efficiency*velociyt ratio
A machine of velocity ratio of 5 requires 10000J of work to raise a load of 600N through a verticol distance of 1.25m .
Find:
i)The work output
ii)The efficiency of the machine
iii)The mechanical advantage of the machine
To find the answers to the given problem, we can use the following formulas:
i. Work Output (W_output) = Work Input (W_input)
ii. Efficiency (η) = W_output / W_input
iii. Mechanical Advantage (MA) = Load / Effort
Given:
Velocity Ratio (VR) = 5
Load (L) = 600N
Distance (D) = 1.25m
Step 1: Calculate the Work Input (W_input)
Work Input (W_input) = Load x Distance
W_input = L x D
W_input = 600N x 1.25m
W_input = 750J
Step 2: Calculate the Work Output (W_output)
Since the velocity ratio (VR) is given, we can use the formula:
W_output = VR x W_input
W_output = 5 x 750J
W_output = 3750J
Step 3: Calculate the Efficiency (η)
Efficiency (η) = W_output / W_input
η = 3750J / 750J
η = 5
Step 4: Calculate the Mechanical Advantage (MA)
MA = Load / Effort
MA = L / (W_input / D)
MA = L / (W_input / D)
MA = 600N / (750J / 1.25m)
MA = 600N / 600N/m
MA = 1
Answers:
i. Work Output = 3750J
ii. Efficiency = 5 (or 500%)
iii. Mechanical Advantage = 1
To solve this problem, we need to use the formulas for work, efficiency, and mechanical advantage.
i. Work output:
The work output can be calculated using the formula: Work output = Force x Distance.
In this case, the force is the load of 600N, and the distance is the vertical distance of 1.25m.
So, Work output = 600N x 1.25m = 750J.
ii. Efficiency:
Efficiency is defined as the ratio of the work output to the work input, expressed as a percentage.
Efficiency = (Work output / Work input) x 100%
To find the efficiency, we need to calculate the work input first.
To calculate the work input, we need to use the formula: Work input = Force x Distance.
In this case, the machine has a velocity ratio of 5, which means the distance moved by the force applied is 5 times the distance moved by the load.
Since the load was lifted through a distance of 1.25m, the force was applied through a distance of 1.25m / 5 = 0.25m.
The force applied can be calculated by rearranging the formula: Force = Work input / Distance.
Thus, Force = Work input / 0.25m.
Given that the machine requires 1000J of work to raise a load of 600N, we can write the equation:
1000J = (Work input / 0.25m) x 0.25m.
By canceling the units and rearranging the equation, we get:
Work input = (1000J x 0.25m) / 0.25m.
So, Work input = 1000J.
Now, we can substitute the values into the efficiency formula:
Efficiency = (Work output / Work input) x 100% = (750J / 1000J) x 100% = 75%.
Therefore, the efficiency of the machine is 75%.
iii. Mechanical advantage:
The mechanical advantage can be calculated using the formula: Mechanical Advantage = Load / Effort.
In this case, the load is 600N.
As the machine has a velocity ratio of 5, the effort can be calculated by dividing the load by the velocity ratio.
Effort = Load / Velocity ratio = 600N / 5 = 120N.
Finally, we can substitute the values into the mechanical advantage formula:
Mechanical Advantage = Load / Effort = 600N / 120N = 5.
Therefore, the mechanical advantage of the machine is 5.