Need all steps: Show loss of mechanical energy is given by [mv²sinYcosY]/(2sin(X+Y))

[Kitimbo]

Need all steps: Show loss of mechanical energy is given by [mv²sinYcosY]/(2sin(X+Y))

A particle of mass,m is projected up of a plane of inclination X° with velocity,v .If the angle of friction is Y°,find how far up the plane it goes before coming to rest.Show that the loss in mechanical energy during this motion is [mv²sinYcosY]/(2sin(X+Y)).
Determine the velocity of the particle when it returns to the point of projection.



Forgive me for not showing any working but I don't know where to start since I don't offer physics but this question was set in the applied math exam.

 

[Deleted member 4993]

A particle of mass,m is projected up of a plane of inclination X° with velocity,v .If the angle of friction is Y°,find how far up the plane it goes before coming to rest.Show that the loss in mechanical energy during this motion is [mv²sinYcosY]/(2sin(X+Y)).
Determine the velocity of the particle when it returns to the point of projection.



Forgive me for not showing any working but I don't know where to start since I don't offer physics but this question was set in the applied math exam.

Start with conservation of energy:

Initial total energy = Instantaneous total energy + friction loss

where

total energy = Potential energy (m * g * h) + kinetic energy (1/2 * m * v²)

Friction loss = frictional force * distance travelled

 

[stapel]

A particle of mass,m is projected up of a plane of inclination X° with velocity,v .If the angle of friction is Y°,find how far up the plane it goes before coming to rest.Show that the loss in mechanical energy during this motion is [mv²sinYcosY]/(2sin(X+Y)).
Determine the velocity of the particle when it returns to the point of projection.

Forgive me for not showing any working but I don't know where to start... this question was set in the applied math exam.

Hasn't your applied-math class covered this material? :shock: