Inclined plane calculator in physics to find friction force, normal force, tension force and acceleration of an object on an inclined plane which is attached to a pulley with a hanging mass. It's assumed that the string has negligible mass and pulley is frictionless. There is a friction between the object and the plane.
Maximum frictional force when the object is not moving and in static condition:
Formulas for object-1 just about to start motion in +x direction:
Newton’s second law for object-2:
Newton’s second law for object-1:
If following condition is met, than the object-1 starts to move in +x direction.
Formulas for object-1 just about to start motion in -x direction:
If following condition is met, than the object-1 starts to move in -x direction.
Formulas for object-1 that is accelerating in +x direction
Maximum frictional force when the object is moving:
$$T{ -m }_{ 1 }g\sin { \alpha } -{ \mu }_{ k }{ m }_{ 1 }g\cos { \alpha } ={ m }_{ 1 }a$$
$${ m }_{ 2 }g-T={ m }_{ 2 }a$$
If these two equations are solved together, than
Formulas for object-1 that is accelerating in -x direction:
$${ m }_{ 1 }g\sin { \alpha }-T -{ \mu }_{ k }{ m }_{ 1 }g\cos { \alpha } ={ m }_{ 1 }a$$
$$T{ -m }_{ 2 }g={ m }_{ 2 }a$$
Note: Use dot "." as decimal separator.
Note: Default rounding is 7 decimal places.
The box shown has mass 5 kg and lies on a plane tilted at an angle of 34° to the horizontal. What is the speed of the object at the bottom of the inclined plane if the box starts from the rest 1.25m up the plane from its base?
Solution:
The speed at the bottom of inclined plane is 2.56734 m/s.