Kinetic Fricion Acceleration Problem

[laxxie]

Homework Statement

To move a large crate across a rough floor, you push on it with a force at an angle of 21 degrees, find the acceleration of the crate if the applied force is 400 , the mass of the crate is 32 and the coefficient of kinetic friction is 0.43.

A = ?
Force = 400N
Theta = 21 Degrees
Mass = 32Kg
Kin fricion coefficient = .43

Homework Equations

Force of Kinetic Friction = Kinetic Friction Coefficient x Normal Force
and probably some random 2 dimension kinematics equation to solve for acceleration...

The Attempt at a Solution

I basically know that if you are pushing down on the box at an angle of 21 degrees than you are basically adding to the weight of hte box and therefore increasing the normal force acting on the box so I did cos21 * 400 + 32kg*9.81 to get the normal force and we already have the static fricion coefficient so then I just multiplied those together to get the kinetic friction force which is wrong so I'm not sure what mistake I'm making here. If you guys could help me out that would be great my teacher is awful and I need to learn this.

 

[planck42]

What are you trying to find?

EDIT: nvm; I figured it out, but PhanthomJay can have this one.

 

[PhanthomJay]

If the angle of the applied force is 21 degrees with the horizontal, then it's 400*sin21 that must be added to the weight. If the angle of the applied force is 21 degrees with the vertical, then your calculation for the kinetic friction force, acting opposite the motion , is correct. But then you have to find the acceleration using Newton's 2nd law, where the sum of forces in x direction (that is, the net force in the x direction) = ma, where the net force is always in the direction of the acceleration.

 

[laxxie]

Thanks, was using wrong trig function haha

 

[rwisz]

I would approach this problem by first identifying the known quantities and the unknown quantity. In this case, the known quantities are the applied force (400N), the angle (21 degrees), the mass (32kg), and the coefficient of kinetic friction (0.43). The unknown quantity is the acceleration of the crate.

Next, I would utilize the equations for force and acceleration to solve for the unknown quantity. The equation for force is F=ma, where F is the applied force, m is the mass, and a is the acceleration. In this case, the applied force includes both the pushing force and the force of kinetic friction, so the equation can be written as F - Fk = ma, where Fk is the force of kinetic friction.

To find the force of kinetic friction, we can use the equation Fk = μkN, where μk is the coefficient of kinetic friction and N is the normal force. The normal force can be calculated by multiplying the mass by the acceleration due to gravity (9.81 m/s^2) and adding to it the component of the applied force in the vertical direction (cos21 * 400N).

Putting it all together, we get the equation (F - μkN) = ma. Substituting in the known values, we get (400N - 0.43 * (32kg * 9.81m/s^2 + cos21 * 400N)) = 32kg * a. Solving for a, we get a = 1.35 m/s^2.

Therefore, the acceleration of the crate is 1.35 m/s^2. It is important to note that this is the net acceleration, as the applied force is balanced by the force of kinetic friction. This means that the crate will continue to move at a constant velocity unless acted upon by an external force.