A man used a rod of length 5.00m to lift a 700kg marble. the fulcrum is 0.50m from the end of the bar that is under the marble calculate the M.A and minimum effort required to lift the load of the efficiency of this system is 90% determine its V.R. what class of lever does this system belong to.
To solve this problem, we need to apply the concept of leverage and the equations related to it.
First, let's define the terms:
- Length of the rod (effort arm): 5.00 m
- Distance from the fulcrum to the load (resistance arm): 0.50 m
- Mass of the marble (load): 700 kg
- Efficiency of the system: 90%
1. Mechanical Advantage (M.A):
The mechanical advantage is determined by the ratio of effort arm length to resistance arm length. It represents the factor by which a lever increases the applied force. The formula to calculate M.A is:
M.A = effort arm length / resistance arm length
In this case, the effort arm length is 5.00 m and the resistance arm length is 0.50 m.
M.A = 5.00 m / 0.50 m = 10
So, the mechanical advantage is 10.
2. Minimum Effort:
To calculate the minimum effort required to lift the load, we can use the formula:
Minimum Effort = Load / M.A
In this case, the load is 700 kg and the M.A is 10.
Minimum Effort = 700 kg / 10 = 70 kg
Therefore, the minimum effort required to lift the load is 70 kg.
3. Efficiency:
Efficiency is defined as the ratio of output work to input work. In this case, the input work is the effort (force) applied to lift the load, and the output work is the work done in lifting the load. The formula to calculate efficiency is:
Efficiency = (Output Work / Input Work) * 100
Since the efficiency is given as 90%, we can rewrite the formula as:
90 = (Output Work / Input Work) * 100
Solving for Output Work / Input Work:
Output Work / Input Work = 90 / 100 = 0.9
So, the output work is 0.9 times the input work.
4. Velocity Ratio (V.R):
The velocity ratio is a measure of how much the speed or distance at one end of the lever is multiplied or divided in comparison to the other end. It is represented by the ratio of the effort arm length to the resistance arm length. The formula to calculate V.R is:
V.R = effort arm length / resistance arm length
In this case, the effort arm length is 5.00 m and the resistance arm length is 0.50 m.
V.R = 5.00 m / 0.50 m = 10
Therefore, the velocity ratio is 10.
5. Class of Lever:
Based on the positions of the fulcrum, load, and effort, this system belongs to the class of levers known as first-class levers. In a first-class lever, the fulcrum is located between the load and the effort.
To summarize:
- Mechanical Advantage (M.A) = 10
- Minimum Effort = 70 kg
- Velocity Ratio (V.R) = 10
- Class of Lever = First-class lever