Newton's second law cosine and sine

[DmytriE]

Newton's second law is taking my mind for a spin and for some reason had me contemplating how it works for several hours. This is all with respect to an incline and an object sitting on the incline with no friction. If the problem does not give you the mass of the object can you completely just ignore the mass and work with just F=gsin(theta)?

Also how do you determine what is mg*sin(theta) and what is mg*cos(theta)? Here is a link to the standard picture of an object on an incline with the arrows drawn in.

http://www.wellesley.edu/Physics/phyllisflemingphysics/107_s_workenergy_images/figure_for13.gif

How you you know that the opposite of the normal force has a cosine rather than sine? I know this law is simplistic but I just can't wrap my head around it. The three letters don't give me much to work with.

 

[Doc Al]

Newton's second law is taking my mind for a spin and for some reason had me contemplating how it works for several hours. This is all with respect to an incline and an object sitting on the incline with no friction. If the problem does not give you the mass of the object can you completely just ignore the mass and work with just F=gsin(theta)?

Almost. The force parallel to the incline depends on the mass (F = mgsinθ), but since a = F/m, the acceleration does not: a = gsinθ.

As far as whether to use sinθ or cosθ, you need to review your trig and the definitions of sine and cosine. Review how trig is used to find the components of vectors. Read these links: http://www.physicsclassroom.com/Class/vectors/U3L3b.cfm"

 

[astrokreng]

I can provide a clear and concise explanation for the concepts mentioned in this content. Firstly, Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be mathematically represented as F=ma, where F is the net force, m is the mass of the object, and a is the acceleration.

In the context of an object on an incline, the force of gravity acting on the object can be broken down into two components - one parallel to the incline (mg*sin(theta)) and one perpendicular to the incline (mg*cos(theta)). This is because the force of gravity always acts towards the center of the Earth, and when on an incline, this force can be resolved into two components along the incline and perpendicular to it.

When the problem does not provide the mass of the object, we can still use Newton's second law by assuming that the mass is a constant and canceling it out from both sides of the equation. This leaves us with F=ma=mg*sin(theta), where m is no longer a variable.

To determine which component of the force of gravity is represented by mg*sin(theta) and mg*cos(theta), we can use the standard picture of an object on an incline with arrows drawn in, as shown in the provided link. The arrow pointing down the incline represents the component of gravity acting along the incline, which is mg*sin(theta). The arrow perpendicular to the incline represents the component of gravity acting perpendicular to the incline, which is mg*cos(theta).

The normal force, which is the force exerted by the incline on the object to prevent it from sinking into the incline, has a cosine component rather than a sine component because it acts perpendicular to the incline. This means that it is directly proportional to the component of gravity acting perpendicular to the incline, which is mg*cos(theta).

In summary, Newton's second law and the concept of resolving forces into components can be applied to understand and solve problems involving objects on inclines. It is important to carefully consider the direction and magnitude of forces, as well as their components, in order to accurately apply this law.