How Do You Apply Newton's Law to Solve Incline Problems?

[r3dxP]

well, my question isn't directly towards Newton's law or anythiing, but its a question on how to solve problems using Newton's law.
for example, look at this problem below..

a force of 20N acts horizontally on a mass of 10kg being pushed up a fritionless incline that makes a 30degrees angle with the horizontal. What is the magnitude of the acceleration of the mass up the incline equal to?

ok, for this problem, how would you know you solve this problem by using the equilibrium in respect to the x ? is it because only x equilibrium exists? or is it because its asking for the magnitude of the acceleration up the incline?
sorry if this question confuses you..

 

[HallsofIvy]

The problem specifically asks for acceleration! There is no equilibrium here.

Break the horizontal force into components, one parallel to the incline, the other perpendicular to it. Only the force parallel to the incline will move the mass up the incline. Also break the vertical gravity force into those same components- one parallel to the incline, the other perpendicular to it. Again, only the component parallel to the incline is important. The net force, up or down the incline, is the parallel component of the force applied minus the parallel component of gravitational force. Then, of course, use F= ma.

 

[quicknote]

Hello,

Thank you for your question about solving problems using Newton's law. In order to solve this particular problem, we first need to understand the forces acting on the mass on the incline. The force of 20N is acting horizontally, while the weight of the mass (10kg x 9.8m/s^2 = 98N) is acting vertically downwards. Since the incline is frictionless, there is no force acting against the motion of the mass.

To find the magnitude of the acceleration up the incline, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In this case, the net force acting on the mass is the horizontal force of 20N. Since we are looking for the acceleration up the incline, we can use the component of the weight force that is acting in that direction, which is equal to (98N x sin 30° = 49N). This means that the net force acting on the mass is equal to 20N - 49N = -29N (since the direction of the weight force is opposite to the direction of the horizontal force).

Now, using Newton's second law, we can solve for the acceleration of the mass: a = F/m = -29N/10kg = -2.9m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the horizontal force, which is up the incline. Therefore, the magnitude of the acceleration is equal to 2.9m/s^2.

To answer your question about using equilibrium in respect to the x-direction, this is because the problem is only asking for the magnitude of the acceleration up the incline, which is in the x-direction. If the problem had asked for the net force or acceleration in a different direction, we would have to consider the forces acting in that direction as well.

I hope this helps to clarify the process of solving problems using Newton's law. Let me know if you have any further questions or need any additional clarification. Good luck with your studies!

Best,