A body of mass 7.5kg is to be pulled up along a place which is inclined at 30degree to the horizontal.if the efficiency of the place is 75%, what is the minimum force required to pull the body of the plwane g=10m/s
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To find the minimum force required to pull the body up the inclined plane, we can start by calculating the weight of the body, which is given by the formula:
Weight = mass * gravitational acceleration
Given that the mass of the body is 7.5 kg and the gravitational acceleration is 10 m/s², we have:
Weight = 7.5 kg * 10 m/s²
= 75 N
Next, we need to find the force required to pull the body up the inclined plane. This force can be calculated using the formula:
Force = Efficiency * Weight
Given that the efficiency of the inclined plane is 75% (or 0.75 in decimal form), we have:
Force = 0.75 * 75 N
= 56.25 N
Therefore, the minimum force required to pull the body up the inclined plane is 56.25 N.
To find the minimum force required to pull the body up the inclined plane, we need to consider the following factors: the weight of the body (mg), the angle of inclination (θ), and the efficiency of the inclined plane.
1. Calculate the weight of the body:
The weight of the body (mg) is given by the formula:
Weight = mass (m) × gravitational acceleration (g)
Weight = 7.5 kg × 10 m/s^2
Weight = 75 N
2. Determine the effective weight along the inclined plane:
The effective weight of the body along the inclined plane is given by the formula:
Effective Weight = Weight × cos(θ)
θ = 30 degrees (given in the question)
Effective Weight = 75 N × cos(30°)
Effective Weight = 75 N × √3/2
Effective Weight = 75 N × 0.866 (approx.)
Effective Weight = 64.95 N (approx.)
3. Calculate the minimum force required to pull the body up the inclined plane:
Since the efficiency of the inclined plane is given as 75%, we need to consider the efficiency factor while calculating the minimum force.
Efficiency = (Output work/Input work) × 100
75% = (Output work/Input work) × 100
We can write the efficiency equation as:
0.75 = (Output work)/(Input work)
The output work is the work done against gravity (Effective Weight × Distance). The input work is the force required (minimum force) multiplied by the distance.
Now, let's assign some values to the distance:
Let's assume the distance is 1 meter.
Output work = Effective Weight × Distance = 64.95 N × 1 m = 64.95 N-m (approx.)
Using the efficiency equation, we can now rewrite it as:
0.75 = (64.95 N-m)/(Minimum force × 1 m)
Cross-multiplying:
Minimum force = (64.95 N-m)/(0.75)
Therefore, Minimum force = 86.6 N (approx.)
So, the minimum force required to pull the body up the inclined plane is approximately 86.6 N.