How would you do this physics problem. Jus equations?

Question

I don't need answers I am just stuck on how to formulate the correct equation

The magnitudute of each force is 164 N the fore on the right is applied at an angle of 44 degrees. he mass of an object is 16 kg
The coefficient of friction is .268 the acceleration of gravity is 9.8m/s/s

Find the resulting acceleration

the second problem


An 863N crate is being pushed across level floor by a force of 313 N at an agle of 21 degrees above the horizontal. The coefficient of kinetic friction between the crate and the floor is .2 the acceleration of the gravity is 9.81 m/s/s

What is the acceleration of the box?


Thank you for any help

I DO NOT NEED AN ANSWER, JUST HOW WOULD I MANIPULATE THE EQUATIONS TO SOLVE THESE PROBLEMS THANK YOU

Answer 1

Consider a body lying at rest on the ground.Let the coefficient of kinetic friction be μ(I am taking kinetic friction because there's no acceleration when static friction acts).Let its mass be m.If a force F acts on it at an angle ϑ to the horizontal,
http://farm3.static.flickr.com/2322/1521111197_b6ae98d169.jpg?v=0
the vector of the force can be resolved into 2 components:
a horizontal component=Fcosϑ which attempts to move the body along the floor
a vertical component=Fsinϑ which acts vertically downwards along gravity
Therefore normal reaction=weight of the body+vertical component of the force acting on it
=mg+Fsinϑ
Frictional force=μ(mg+Fsinϑ)
Net force acting on the body=Fcosϑ-frictional force
=Fcosϑ-μ(mg+Fsinϑ)
acceleration={ Fcosϑ-μ(mg+Fsinϑ) }/m

Answer 2

I don't understand the first question, but I can help with the second and that might give you the help you need.

The first thing you need to worry about in any problem that involves friction is the normal force, the force perpendicular to the surface experiencing the friction.

In this case, surface (floor) is level so the normal force is force pointing down.

There are two parts to the normal force N: the part that comes from gravity and the part that comes from the pushing force.

N = Gn + Pn

Gravity is operating normal to the surface so Gn is just the weight in the specified gravitational field. (Force = mass times acceleration; you have the mass and the acceleration due to gravity)

The pushing force P is operating at an angle. You need to separate this force into the horizontal and vertical components, Ph and Pv.

What is not clear from the description is whether P is pushing up and across at an angle of 21 degrees or down and across at 21 degrees. The Ph is the same in both cases, but in the first case Pv points up (opposite gravity) and in the other it points down (adding to gravity)

Once you decide this, you can compute N. (Pn is either the same as Pv or the same as -Pv.)

Now that you have N you can compute the horizontal force due to friction, call it K. This K is just N times the coefficient of kinetic friction.

Compare this with the value of Ph, the horizontal pushing force. If Ph is greater, the net horizontal force is the difference (Ph - K) (friction always operates against the direction of motion).

So you have the mass and the net horizontal force, and you know that force = mass x acceleration so you can compute
acceleration = force/mass

(If K is greater than Ph, then there is too much friction to move the box so the acceleration has to be 0. :-)

HTH.