Can anyone help me with this question? Consider that a particle of mass M is fired thanks to compression d in a spring of elastic constant k the mass slides through a horizontal surface without friction, then passes through a radius loop r and finally rises in an inclined plane an angle e
A) Determine what condition must be met in terms of compression of spring d, to ensure that the particle will be met.

B)Find an expression that allows to calculate the height h to which the particle of mass M reaches on the inclined plane.

The spring potential energy must equal or exceed the energy to raise the mass to loop height and the minimum kinetic energy needed to keep the mass in contact with the top of the loop

kd² = 5Mrg

h = kd²/2Mg

Explanation:

at top of loop

Mv²/r = Mg

v² = rg

½kd² = ½Mv² + Mgh'

½kd² = ½M(rg) + Mg(2r)

½kd² = 2.5Mrg

kd² = 5Mrg

½kd² = Mgh

h = kd²/2Mg

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

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