A rough 4cm long plank is used road an inclined plane to raise a 500N bag up to the floor of a long lorry 2m high. 200j of work is done against friction between the bag and the plank.calculate (a) the total work done by effort (b) the efficiency of the inclined plane (c) the effort needed to pull the bag up the plane.
(a) The total work done by the effort can be calculated using the formula:
Work = Force × Distance
In this case, the force is the weight of the bag, which is 500N, and the distance is the height the bag is raised, which is 2m. Therefore:
Work = 500N × 2m = 1000J
So, the total work done by the effort is 1000J.
(b) The efficiency of the inclined plane can be calculated using the formula:
Efficiency = (Output Work / Input Work) × 100%
In this case, the output work is the work done against friction, which is given as 200J. The input work is the total work done by the effort, which is 1000J. Therefore:
Efficiency = (200J / 1000J) × 100% = 20%
So, the efficiency of the inclined plane is 20%.
(c) The effort needed to pull the bag up the plane can be calculated using the formula:
Effort = Work / Distance
In this case, the work is the total work done by the effort, which is 1000J, and the distance is the length of the inclined plane, which is given as 4cm (0.04m). Therefore:
Effort = 1000J / 0.04m = 25000N
So, the effort needed to pull the bag up the plane is 25000N.
Hope that answers your question!
To calculate the requested values, we'll use the following formulas:
1. Work = Force x Distance
2. Efficiency = (Useful work output / Total work input) x 100%
Let's calculate each value step by step:
(a) The total work done by effort:
In this case, the total work done by effort refers to the work done against friction between the bag and the plank.
Given:
Force = 200 N
Distance = 4 cm = 0.04 m (converted to meters)
Using the formula for work, we have:
Work = Force x Distance
Work = 200 N x 0.04 m
Work = 8 J
So, the total work done by effort is 8 J.
(b) The efficiency of the inclined plane:
Efficiency is given by the formula:
Efficiency = (Useful work output / Total work input) x 100%
Useful work output in this case refers to the work done on the 500 N bag to raise it to the height of the lorry. Total work input refers to the work done by the effort.
Given:
Useful work output = Work done on the 500 N bag = Force x Distance = 500 N x 2 m = 1000 J (since the distance is given as 2m)
Total work input = Work done by effort = 8 J (calculated in step a)
Using the efficiency formula, we have:
Efficiency = (Useful work output / Total work input) x 100%
Efficiency = (1000 J / 8 J) x 100%
Efficiency ≈ 12500%
Therefore, the efficiency of the inclined plane is approximately 12500%.
(c) The effort needed to pull the bag up the plane:
The effort needed refers to the force required to overcome the weight of the 500 N bag.
The weight of the bag is given as 500 N, which is also the force required to lift the bag against gravity. Therefore, the effort needed to pull the bag up the inclined plane is 500 N.
To calculate the total work done:
a) The work done against friction can be calculated using the formula: Work = Force × distance.
Given:
Force against friction = 200 J
Distance = 4 cm = 0.04 m
Substituting the values into the formula, we get:
Work against friction = 200 J = Force against friction × 0.04 m
Now we can rearrange the formula to solve for Force against friction:
Force against friction = Work against friction / Distance
Substituting the values, we get:
Force against friction = 200 J / 0.04 m = 5000 N
The total work done by effort can be calculated by adding the work done against friction to the work done against gravity:
Total work done by effort = Work against friction + Work against gravity
The work done against gravity can be calculated using the formula: Work = Force × distance.
Given:
Force against gravity = weight (mass × acceleration due to gravity) = 500 N
Distance = 2 m
Substituting the values into the formula, we get:
Work against gravity = 500 N × 2 m = 1000 J
Now we can calculate the total work done by effort:
Total work done by effort = 200 J + 1000 J = 1200 J
b) The efficiency of the inclined plane can be calculated using the formula: Efficiency = (useful work output / total work input) × 100%.
The useful work output is the work done against gravity, which is 1000 J.
The total work input is the total work done by effort, which is 1200 J.
Substituting the values into the formula, we get:
Efficiency = (1000 J / 1200 J) × 100% = 83.33%
c) The effort needed to pull the bag up the plane can be calculated using the formula: Effort = Force required × distance.
Given:
Force required = weight (mass × acceleration due to gravity) = 500 N
Distance = 2 m
Substituting the values into the formula, we get:
Effort = 500 N × 2 m = 1000 J
Therefore, the effort needed to pull the bag up the inclined plane is 1000 J.
total work=friction+ PEgained= 200j+500*2 j= 1200j
efficiency=workout/workin= 1000/1200
effort*distance=workin
effort=1200/ lengthofPlank I am wondering if your 4 cm should be 4 m.