- #1
Loren Booda
- 3,125
- 4
Derive the slope of a track where a sphere having frictional coefficient u maintains constant velocity v.
Assuming the sphere rolls without slipping, this looks good.Gamma said:If I use Torque = I * alpha and Newtons second law, I end up with the following for acceleration.
a = mg sin(theta) * r^2 /(I + mr^2) where I is w.r.t. the center of the rolling object.
Not sure what you did here. Realize that as long as the sphere rolls without slipping, the friction does no work.If I use the energy relation (i.e Change in Energy = work done by the force), I get
a = g[2 sin (theta) + u cos(theta)] / ( 1 + I/mr^2)
Constant velocity on a frictional slope refers to an object moving at a constant speed on a slope with friction present. This means that the object's speed does not change, and it is not accelerating or decelerating.
The main difference is the presence of friction. On a flat surface, there is typically less friction, so an object can maintain a constant velocity with minimal effort. On a frictional slope, the object must overcome the force of friction to maintain a constant speed.
The main factors that affect constant velocity on a frictional slope are the mass of the object, the angle of the slope, and the coefficient of friction between the object and the surface.
In theory, yes. If there are no external forces acting on the object and the conditions remain constant, the object can maintain a constant velocity on a frictional slope forever. However, in real-world scenarios, there are always external factors that can affect the object's velocity, such as air resistance or changes in surface conditions.
To calculate the velocity of an object on a frictional slope, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the acceleration would be equal to the force of gravity minus the force of friction. We can also use the equations of motion to calculate the velocity at specific points along the slope.