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.
A 20KG MASS IS TO BE PULLED UP A SLOPE INCLINED AT 30 TO THE HORIZONTAL IF THE EFFICIENCY OF THE PLANE IS 75% FIND THE FORCE REQUIRED TO PULL THE LOAD UP THE PLANE
To find the force required to pull the load up the inclined plane, we'll need to consider the forces acting on the mass.
Here are the steps to find the force required:
1. Draw a free body diagram of the mass showing all the forces acting on it. In this case, there are three forces: the gravitational force (mg), the normal force (N), and the force required to pull the load up the plane (F).
2. Resolve the forces into components. Since the slope is inclined at 30 degrees to the horizontal, we'll need to consider the components of the forces along the slope and perpendicular to the slope.
3. Determine the weight of the object. The weight (mg) acts vertically downwards and can be resolved into two components: one along the slope (mgsinθ) and one perpendicular to the slope (mgcosθ). Here, θ represents the angle of inclination (30 degrees).
4. Find the value of the normal force (N). The normal force acts perpendicular to the slope and is equal in magnitude but opposite in direction to the perpendicular component of the weight (mgcosθ). Therefore, N = mgcosθ.
5. Calculate the force required to pull the mass up the slope. The force required (F) can be determined by considering the equilibrium of forces along the slope. The force required is equal to the parallel component of the weight (mgsinθ) plus the frictional force (μN), where μ is the coefficient of friction.
6. Apply the formula for efficiency. 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 required to overcome gravity (mgsinθ). The formula for efficiency is given by:
Efficiency = (useful work output / total work input) * 100%
Rearranging the formula, the force required can be expressed as:
F = (Efficiency / 100%) * total work input
7. Substitute the given values into the formula. We know that efficiency is 75% (or 0.75) and the total work input is mgsinθ.
F = (0.75) * mgsinθ
8. Plug in the known values. Given that the mass (m) is 20 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the angle of inclination (θ) is 30 degrees, we can calculate the force required.
F = (0.75) * (20 kg) * (9.8 m/s²) * sin(30°)
Simplifying this calculation will give you the force required to pull the load up the inclined plane.
Wm = 20 kg * 9.8 N./kg = 196 N. = Weight of mass.
Fm = 196 N. @ 30 Deg. = Force of mass.
Fp = 196*sin30 = 98 N. = Force parallel
to plane.
Fv = 196*cos30 = 169.7 N. = Force perpendicular to plane.
Fn = 0.75Fap - Fp = 0,
0.75Fap - 98 = 0,
0.75Fap = 98,
Fap = 130.7 N. = Force applied.
M*g = 20 * 9.8 = 196 N.
Fap = 196*sin30/0.75 = 130.7 N. = Force applied.