Finding Friction force impeding boxs motion

[cleo0724]

A 21.0 kg box is released on a 36.0° incline and accelerates down the incline at 0.271 m/s2. Find the friction force impeding its motion.

F=mg*cos(36)

F=21(9.8)*cos(36)
F=205.8*.809
F=166.495

I'm not sure what I'm doing wrong. Please help

 

[rock.freak667]

the component of the weight acts downwards and the friction acts upwards (directions are parallel to the plane)


so if the box moves down then ma=forces down-forces up.


a bit easier now?

 

[kerimek]

Hello,

Based on the given information, it seems like you are on the right track to finding the friction force impeding the box's motion. However, there are a few things that may be causing confusion.

First, I noticed that you used the formula F=mg*cos(36) to calculate the friction force. This formula is actually used to calculate the component of the weight (mg) that is acting parallel to the incline. In this case, we are looking for the total friction force, not just the component parallel to the incline.

To find the total friction force, we can use the formula F=μN, where μ is the coefficient of friction and N is the normal force. The normal force is the force that the incline exerts on the box perpendicular to the surface. In this case, the normal force is equal to the weight of the box (mg) multiplied by the cosine of the incline angle (cos(36)).

So, the correct formula to use would be F=μmg*cos(36). However, we still need to determine the coefficient of friction (μ) in order to calculate the friction force.

To do this, we can use the given information about the box's acceleration. We know that the box is accelerating down the incline at 0.271 m/s^2. This acceleration is caused by the net force acting on the box, which is equal to the weight of the box (mg) minus the friction force (F). So, we can set up the following equation:

F=mg-ma

Substituting in the values we know, we get:

F=21(9.8)-21(0.271)
F=205.8-5.691
F=200.109

Now, we can plug this value for F into our original formula for friction force, F=μN, to get:

200.109=μ(21*9.8*cos(36))

Solving for μ, we get:

μ=200.109/(21*9.8*cos(36))
μ=0.998

Finally, we can plug this value for μ into our original formula for friction force, F=μmg*cos(36), to get:

F=0.998*21*9.8*cos(36)
F=205.8*0.809*0.998
F=166.513

So, the friction force imp