Effort Applied to Move Body Upward on Inclined Plane Considering Friction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))
Pup = (W*sin(αi+Φ))/sin(θe-(αi+Φ))
This formula uses 1 Functions, 5 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
Variables Used
Effort to Move Upwards Considering Friction - (Measured in Newton) - Effort to Move Upwards Considering Friction is the force applied in a given direction to cause the body to slide with uniform velocity parallel to the plane.
Weight of Body - (Measured in Newton) - Weight of Body is the force acting on the object due to gravity.
Angle of Inclination of Plane to Horizontal - (Measured in Radian) - Angle of inclination of plane to horizontal is formed by the inclination of one plane to another; measured in degrees or radians.
Limiting Angle of Friction - (Measured in Radian) - The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).
Angle of Effort - (Measured in Radian) - Angle of Effort is the angle which the line of action of effort makes with the weight of the body W.
STEP 1: Convert Input(s) to Base Unit
Weight of Body: 120 Newton --> 120 Newton No Conversion Required
Angle of Inclination of Plane to Horizontal: 23 Degree --> 0.40142572795862 Radian (Check conversion here)
Limiting Angle of Friction: 2 Degree --> 0.03490658503988 Radian (Check conversion here)
Angle of Effort: 85 Degree --> 1.4835298641949 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pup = (W*sin(αi+Φ))/sin(θe-(αi+Φ)) --> (120*sin(0.40142572795862+0.03490658503988))/sin(1.4835298641949-(0.40142572795862+0.03490658503988))
Evaluating ... ...
Pup = 58.559704123303
STEP 3: Convert Result to Output's Unit
58.559704123303 Newton --> No Conversion Required
FINAL ANSWER
58.559704123303 58.5597 Newton <-- Effort to Move Upwards Considering Friction
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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21 Angle Friction Calculators

Effort Applied to Move Body Downward on Inclined Plane Considering Friction
Go Effort to Move Downwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))
Effort Applied to Move Body Upward on Inclined Plane Considering Friction
Go Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied to Move Body Downward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied to Move Body Upward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward
Go Efficiency of Inclined Plane = sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/(sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Upward
Go Efficiency of Inclined Plane = (sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))/sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Parallel to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)-Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Applied Parallel to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)+Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Required to Move Body down Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Effort Required to Move Body up Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/tan(Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Frictional Force between Cylinder and Inclined Plane surface for Rolling without Slipping
Go Force of Friction = (Mass of Cylinder*Acceleration due to Gravity*sin(Angle of Inclination))/3
Effort Applied Perpendicular to Inclined Plane to Move Body along Inclination Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal)
Effort Applied Parallel to Inclined Plane to Move Body Upward or Downward Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*sin(Angle of Inclination of Plane to Horizontal)
Limiting Angle of Friction
Go Limiting Angle of Friction = atan(Limit Force/Normal Reaction)
Angle of Repose
Go Angle of Repose = atan(Limiting Force/Normal Reaction)
Minimum Force Required to Slide Body on Rough Horizontal Plane
Go Minimum Effort = Weight of Body*sin(Angle of Effort)
Coefficient of Friction between Cylinder and Surface of Inclined Plane for Rolling without Slipping
Go Coefficient of Friction = (tan(Angle of Inclination))/3

Effort Applied to Move Body Upward on Inclined Plane Considering Friction Formula

Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))
Pup = (W*sin(αi+Φ))/sin(θe-(αi+Φ))

Does an inclined plane change the direction of the force?

Inclined planes, also referred to as ramps, are a type of simple machine which manipulate the direction and magnitude of a force. Inclined planes, like all other simple machines, use mechanical advantage which is the ratio of the output force to the applied force.

How to Calculate Effort Applied to Move Body Upward on Inclined Plane Considering Friction?

Effort Applied to Move Body Upward on Inclined Plane Considering Friction calculator uses Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)) to calculate the Effort to Move Upwards Considering Friction, Effort Applied to Move Body Upward on Inclined Plane considering Friction is the force required for the upward motion of a body on an inclined plane. Effort to Move Upwards Considering Friction is denoted by Pup symbol.

How to calculate Effort Applied to Move Body Upward on Inclined Plane Considering Friction using this online calculator? To use this online calculator for Effort Applied to Move Body Upward on Inclined Plane Considering Friction, enter Weight of Body (W), Angle of Inclination of Plane to Horizontal i), Limiting Angle of Friction (Φ) & Angle of Effort e) and hit the calculate button. Here is how the Effort Applied to Move Body Upward on Inclined Plane Considering Friction calculation can be explained with given input values -> 58.5597 = (120*sin(0.40142572795862+0.03490658503988))/sin(1.4835298641949-(0.40142572795862+0.03490658503988)).

FAQ

What is Effort Applied to Move Body Upward on Inclined Plane Considering Friction?
Effort Applied to Move Body Upward on Inclined Plane considering Friction is the force required for the upward motion of a body on an inclined plane and is represented as Pup = (W*sin(αi+Φ))/sin(θe-(αi+Φ)) or Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)). Weight of Body is the force acting on the object due to gravity, Angle of inclination of plane to horizontal is formed by the inclination of one plane to another; measured in degrees or radians, The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN) & Angle of Effort is the angle which the line of action of effort makes with the weight of the body W.
How to calculate Effort Applied to Move Body Upward on Inclined Plane Considering Friction?
Effort Applied to Move Body Upward on Inclined Plane considering Friction is the force required for the upward motion of a body on an inclined plane is calculated using Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)). To calculate Effort Applied to Move Body Upward on Inclined Plane Considering Friction, you need Weight of Body (W), Angle of Inclination of Plane to Horizontal i), Limiting Angle of Friction (Φ) & Angle of Effort e). With our tool, you need to enter the respective value for Weight of Body, Angle of Inclination of Plane to Horizontal, Limiting Angle of Friction & Angle of Effort and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Effort to Move Upwards Considering Friction?
In this formula, Effort to Move Upwards Considering Friction uses Weight of Body, Angle of Inclination of Plane to Horizontal, Limiting Angle of Friction & Angle of Effort. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Effort to Move Upwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)+Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
  • Effort to Move Upwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
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