A costant force F iss applied to a crate of mass 25kg to move it upwards along a frictionless inclined plane, when it reaches point A, its speed is 12m.s and 10,8 m,s when it reaches point B which is 3,5m futher up the incline.
5,1 give a reason why the normal force does no work on the crate during its mortion up the incline?
5,2use ENERGY PRINCIPLES to calculate the magnitude of the force F?
5.1: The normal force does no work on the crate during its motion up the incline because the normal force is always perpendicular to the direction of motion. Work is defined as the dot product of force and displacement, and for work to be done, there must be a component of force in the direction of displacement. Since the normal force is always perpendicular to the incline, it has no component in the direction of motion, and therefore, it does no work.
5.2: To calculate the magnitude of the force F using energy principles, we can use the principle of conservation of mechanical energy. The mechanical energy of the crate is given by the sum of its kinetic energy and potential energy.
At point A:
Kinetic Energy = 1/2 * mass * velocity^2
Potential Energy = mass * g * height_A (where g is the acceleration due to gravity)
Total Mechanical Energy at point A = Kinetic Energy + Potential Energy
At point B:
Kinetic Energy = 1/2 * mass * velocity^2
Potential Energy = mass * g * height_B (where g is the acceleration due to gravity)
Total Mechanical Energy at point B = Kinetic Energy + Potential Energy
Since there is no friction, the mechanical energy of the crate is conserved between the two points. Therefore, we can equate the total mechanical energy at point A to the total mechanical energy at point B:
Total Mechanical Energy at point A = Total Mechanical Energy at point B
(1/2 * mass * velocity_A^2) + (mass * g * height_A) = (1/2 * mass * velocity_B^2) + (mass * g * height_B)
Now we can substitute the given values to solve for the magnitude of force F.