A machine with v.r 5 was used to raise a load of 1.2kg mass through high of 10m. If the workdone to raise the load is 800j find usefull work output, find efficiency,and m.a of the machine
Well, well, well! Let's calculate the useful work output, efficiency, and mechanical advantage of this machine!
First, let's find the useful work output. The formula for work is given by:
Work = Force × Distance
Since the machine has a mechanical advantage of 5, it means the machine reduces the force required by a factor of 5. Therefore, the force applied by the machine can be calculated as:
Force = load mass × gravitational acceleration
Force = 1.2kg × 9.8m/s^2 (gravitational acceleration is approximately 9.8m/s^2)
To find the distance over which this force acts, we simply take the height raised, which is 10m.
Now we can calculate the work done by the machine as:
Work = Force × Distance
Work = (1.2kg × 9.8m/s^2) × 10m
So, the useful work output is 117.6 joules.
Next, let's determine the efficiency of the machine. The efficiency is given by the equation:
Efficiency = (Useful work output / Work input) × 100
Given that the work done to raise the load is 800 joules, we can calculate the efficiency as:
Efficiency = (117.6J / 800J) × 100
So, the efficiency of the machine is approximately 14.7%.
Lastly, let's find the mechanical advantage (M.A.) of the machine. As mentioned earlier, the mechanical advantage is 5, since it reduces the force required by a factor of 5.
Therefore, the mechanical advantage (M.A.) of the machine is 5.
There you have it! The useful work output is 117.6 joules, the efficiency is approximately 14.7%, and the mechanical advantage is 5.
To find the useful work output of the machine, we need to first calculate the work done. The work done can be calculated using the formula:
Work = Force x Distance
The force acting on the load can be calculated using Newton's second law of motion:
Force = mass x acceleration
Acceleration can be calculated using the formula:
Acceleration = g x ma (where g is the acceleration due to gravity and ma is the mechanical advantage of the machine)
Given:
Mass of the load (m) = 1.2 kg
Distance (d) = 10 m
Work done (W) = 800 J
V.R (velocity ratio) = 5
Step 1: Calculate the force acting on the load:
Force = mass x acceleration
Given:
Mass = 1.2 kg
Force = 1.2 kg x acceleration
Step 2: Calculate the acceleration:
Acceleration = g x ma
Given:
V.R = 5
Acceleration = g x (V.R)
Acceleration = 9.8 m/s^2 x 5
Step 3: Substitute the values into the force formula:
Force = 1.2 kg x acceleration
Step 4: Calculate the work done using the force and distance:
Work = Force x Distance
800 J = Force x 10 m
Step 5: Solve for the force:
Force = 800 J / 10 m
Step 6: Use the force to determine the useful work output:
Useful Work Output = Force x Distance
Step 7: Calculate the efficiency of the machine:
Efficiency = (Useful Work Output / Work Done) x 100
Step 8: Calculate the mechanical advantage (m.a) of the machine:
m.a = V.R / 100
Now let's calculate the values:
Step 2: Calculate acceleration:
Acceleration = 9.8 m/s^2 x 5 = 49 m/s^2
Step 4: Calculate force:
Force = 800 J / 10 m = 80 N
Step 6: Calculate useful work output:
Useful Work Output = Force x Distance = 80 N x 10 m = 800 J
Step 7: Calculate efficiency:
Efficiency = (Useful Work Output / Work Done) x 100 = (800 J / 800 J) x 100 = 100%
Step 8: Calculate mechanical advantage:
m.a = V.R / 100 = 5 / 100 = 0.05
To summarize:
Useful Work Output = 800 J
Efficiency = 100%
Mechanical Advantage (m.a) = 0.05
To find the useful work output of the machine, we need to determine the work done against gravity by the machine. This can be calculated using the formula:
Work = Force × Distance
The force can be determined by multiplying the mass of the load by the acceleration due to gravity (9.8 m/s²). The distance is given as 10 meters.
Force = mass × acceleration due to gravity
Force = 1.2 kg × 9.8 m/s²
Now, let's calculate the force using the given values:
Force = 1.2 kg × 9.8 m/s² = 11.76 N
Next, we can calculate the useful work output by multiplying the force by the distance:
Useful work output = Force × Distance
Useful work output = 11.76 N × 10 m = 117.6 J
Therefore, the useful work output of the machine is 117.6 joules.
To find the efficiency of the machine, we will use the formula:
Efficiency = (Useful work output / Work input) × 100
The work input can be determined based on the given value of 800 joules.
Efficiency = (117.6 J / 800 J) × 100
Efficiency = 14.7%
Therefore, the efficiency of the machine is 14.7%.
Finally, to calculate the mechanical advantage (M.A) of the machine, we can use the formula:
M.A = Load / Effort
In this case, since both the load and the effort are not given, we can use the equation based on the velocity ratio (V.R):
M.A = V.R / efficiency
Given V.R is 5 and efficiency is 14.7% (0.147), we can solve for M.A:
M.A = 5 / 0.147
M.A ≈ 34.01 (rounded to two decimal places)
Therefore, the mechanical advantage of the machine is approximately 34.01.
work output = m g h = 1.2 * 9.81 * 10 = 117 Joules
efficiency = 117/800 = .147 = 14.7%