inclined slope problem

[kasheee]

A particle P of mass 0.5 kg moves upwards along a line ofgreatest slope of a rough plane inclined at
an angle of 40◦ to the horizontal. P reaches its highest point and then moves backdown the plane.
The coefficient offriction between P and the plane is 0.6

The magnitude of thefrictional force acting on P is2.25N, correct to 3 significant
figures.

(ii) Findthe acceleration of P when it is moving
(a) up the plane,


My working out are -0.5 g sin alpha – f – force going up =ma

... as the weight and friction must be opposing motion, hence there must be another force in the opposite direction.

ButI don’t know the forward force going up? Thanks.

 

[wjm11]

A particle P of mass 0.5 kg moves upwards along a line ofgreatest slope of a rough plane inclined at
an angle of 40◦ to the horizontal. P reaches its highest point and then moves backdown the plane.
The coefficient offriction between P and the plane is 0.6

The magnitude of thefrictional force acting on P is2.25N, correct to 3 significant
figures.

(ii) Findthe acceleration of P when it is moving
(a) up the plane,


My working out are -0.5 g sin alpha – f – force going up =ma

... as the weight and friction must be opposing motion, hence there must be another force in the opposite direction.

ButI don’t know the forward force going up?

You have calculated the friction force correctly. Also, you are correct in stating that the friction force and the tangential gravitational force act against the direction of motion, i.e., they point down the slope.

However, there is no third force pointing up the slope. The object simple has an initial velocity up the slope. The object is not in static equilibrium, so the forces are not balanced, i.e., the net force is not zero. If it were zero, there would be no acceleration and no change in velocity.

So, you have your two forces and you know the mass. a = F/m.

Make sense?

A final note: It is fine to use three significant digits while doing your calculations, but the problem statement only has the COF and mass stated to one sig dig, so only use one significant digit in your answer.