Dynamic Motion: Frictional Forces and slope

[perplexed_in_texas]

In a problem concerning Mechanics/Dynamic Motion, I am asked to find the acceleration net of an unidentified mass. I am given mu (.1) and the slope of the incline (38 degrees). After searching through my notes and as well as online, I cannot seem to find a way to determine the magnitude of the acceleration using only these two pieces of data!

Net Acceleration = Force Applied - Force of Friction / mass

mu = .1
slope incline = 38 degrees

I am aware of how to use trigonometry with Normal Force, gravity, etc., but with only two measurements, I'm drawing up a total blank on how to properly this problem! I sure appreciate yall helping me out on this.

 

[Fermat]

Resolve the mass into components parallel to and perpindicular to the slope

The applied force will be the component of the mass acting down the plane.

The friction force is mu times the normal reaction to the mass by the plane.

 

[quicknote]

Hello,

Thank you for reaching out for assistance with your problem. In order to find the net acceleration of an unidentified mass, we need to take into consideration the forces acting on the mass. In this case, we have the force of friction and the force applied. We can use the formula Net Acceleration = Force Applied - Force of Friction / mass to solve this problem.

First, we need to find the force of friction. This can be done by using the formula Ff = mu * N, where mu is the coefficient of friction and N is the normal force. In this case, we do not have the normal force, but we can use the slope of the incline to find it. The normal force is equal to the weight of the object multiplied by the cosine of the angle of the incline. So, we can find the normal force by calculating N = mg * cos(38 degrees).

Now that we have the normal force, we can find the force of friction by Ff = mu * N. Plugging in the values, we get Ff = 0.1 * (mg * cos(38 degrees)).

Next, we need to find the force applied. This can be done by using the formula Fa = m * a, where m is the mass and a is the acceleration. Since we are trying to find the acceleration, we can rearrange the formula to a = Fa / m.

Now, we can plug in the values we have into the formula Net Acceleration = Force Applied - Force of Friction / mass. We get a = (Fa - Ff) / m.

Substituting the values, we get a = (m * a - 0.1 * (mg * cos(38 degrees))) / m.

We can simplify this to a = a - 0.1 * g * cos(38 degrees).

Finally, we can solve for the acceleration by isolating it on one side of the equation. This gives us a = 0.1 * g * cos(38 degrees).

So, the net acceleration of the unidentified mass is 0.1 * g * cos(38 degrees).

I hope this explanation helps you understand how to solve this problem. If you have any further questions, please don't hesitate to ask. Keep up the good work!

Best,