How Is Friction Force Calculated on an Incline?

[lu6cifer]

1.Quick question: a 12kg mass is on a 30 degree incline where the coefficient of static friction is 0.8. What is the friction force exerted on the mass?



2. F = ma, f = uN



3. I got around 83 N for this. All I did was multiply the coefficient of friction by normal force, which was Wcos30 in this case. So, 0.8 * 12 * 9.81 * cos30, giving me around 83 N, but my answer sheet says 60 N...

 

[PhanthomJay]

Remember, the static friction force is equal to uN only when the object is about to slide relative to the surface. Is it? What is the component of the gravity force acting on the object down the plane?

 

[thomate1]

The friction force is a resistive force that occurs when two surfaces come into contact and slide or attempt to slide against each other. It is caused by the microscopic roughness of the surfaces and the interlocking of these rough surfaces which results in a force that opposes motion.

In this specific scenario, the friction force can be calculated using the formula f=uN, where f is the friction force, u is the coefficient of static friction, and N is the normal force. In this case, the normal force can be calculated as the weight of the object, which is 12kg multiplied by the acceleration due to gravity (9.81 m/s^2) and the cosine of the angle of inclination (30 degrees). This gives a normal force of approximately 103 N.

Plugging in the given values, the friction force can be calculated as f= 0.8 * 103 N, which gives a result of 82.4 N. This is slightly different from the answer of 83 N that you calculated, but it is within a reasonable range of error.

It is possible that the answer sheet used a different value for the acceleration due to gravity or rounded the values differently, resulting in a slightly different answer. It is important to remember that calculations involving friction forces can be affected by small variations and it is common to have slightly different results. However, your calculation method is correct and the answer you obtained is also a valid approximation of the friction force in this scenario.