A 20kg mass is to be pulled up a slope inclined at 30 degree to the horizontal.If the efficiency of the plane is 75% find the force required to pull the load up the plane.
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To find the force required to pull the load up the plane, we need to consider the weight of the load and the angle of the inclination.
First, let's calculate the weight of the load. The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
In this case, the mass of the load is given as 20kg, and the value of acceleration due to gravity (gravitational acceleration) is approximately 9.8 m/s².
Weight = 20 kg × 9.8 m/s²
Weight = 196 N
Now, we need to find the force required to pull the load up the inclined plane. This force can be calculated using the formula:
Force = Weight / (sin θ)
Where θ is the angle of inclination, which is given as 30 degrees.
However, we also need to consider the efficiency of the plane in this scenario. Efficiency is defined as the ratio of useful work output to the total work input. In this case, the useful work output is the force required to pull the load up the plane, and the total work input is the force applied.
The efficiency is given as 75%, which can be expressed as a decimal fraction of 0.75. So, we can write:
Efficiency = useful work output / total work input
0.75 = Force / Force applied
Since we know the efficiency and the force to be applied are related, we can rearrange the equation to solve for the force required to pull the load up the plane.
Force = Efficiency × Force applied
Substituting the known values:
Force = 0.75 × Force applied
Finally, we substitute the value of the weight we calculated earlier for the force applied:
Force = 0.75 × 196 N
Force ≈ 147 N
Therefore, the force required to pull the 20kg load up the inclined plane is approximately 147 Newtons.