The formula for calculating the velocity of a mass moving through a loop with friction is v = √(rg - 2μgh), where v is the velocity, r is the radius of the loop, g is the acceleration due to gravity, μ is the coefficient of friction, and h is the height of the loop.
Friction acts as a resistive force on the mass, slowing it down as it moves through the loop. This means that the velocity of the mass will decrease as the coefficient of friction increases.
No, the velocity of the mass will always decrease due to friction, meaning that it will never be greater than the initial velocity. However, the decrease in velocity may be small enough to be negligible in some cases.
The coefficient of friction can be determined by using the formula μ = Ff/mg, where Ff is the force of friction, m is the mass of the object, and g is the acceleration due to gravity. This value can also be obtained experimentally by measuring the force of friction and the normal force acting on the object.
There are a few ways to increase the velocity of a mass moving through a loop with friction. One way is to decrease the coefficient of friction by using a smoother surface or lubricant. Another way is to increase the initial velocity of the mass or decrease the radius of the loop. Additionally, reducing the height of the loop or increasing the gravitational acceleration can also increase the velocity of the mass.