Hoop rolling down incline

In summary, part A and B of the question asked for the total kinetic energy and velocity of a cylindrical hoop with a radius of 10.0 cm and mass of 0.550 kg rolling a distance of 5.70 m along a board tipped at an angle of 18.0 degrees from horizontal. Part C then asked for the minimum coefficient of static friction needed for the hoop to roll without slipping. To solve this, a free body diagram must be drawn and Newton's 2nd law for both rotation and translation must be applied.
  • #1
Zach981
7
0
This a question from my 131 "masteringphysics.com" hw.

A cylindrical hoop has radius 10.0 cm and mass 0.550 kg. It rolls from rest a distance of 5.70 m along a board which is tipped up by an angle 18.0 degrees from horizontal. Regard the hoop as being much thinner (in the radial direction) than its radius.

Parts A and B wanted me to find the total kinetic energy and velocity at the base of the incline, I already did these. KE = 9.49 J and v=4.15 m/s

However part C wants me to:
What minimum value must the coefficient of static friction have if the hoop is to roll without slipping?
I have no idea how to approach this part.
 
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  • #2
Start by drawing a free body diagram showing all forces acting on the hoop. Then apply Newton's 2nd law for both rotation and translation.
 

Related to Hoop rolling down incline

What is hoop rolling down incline?

Hoop rolling down incline is a physical phenomenon where a cylindrical hoop or ring rolls down an inclined plane due to the force of gravity. The motion of the hoop is affected by factors such as the angle of the incline, the mass and diameter of the hoop, and the coefficient of friction between the hoop and the inclined surface.

What is the formula for calculating the speed of a hoop rolling down an incline?

The formula for calculating the speed of a hoop rolling down an incline is given by v = √(2gh(sinθ + μcosθ)), where v is the speed of the hoop, g is the acceleration due to gravity, h is the height of the incline, θ is the angle of the incline, and μ is the coefficient of friction.

How does the angle of the incline affect the speed of the hoop?

The angle of the incline affects the speed of the hoop because it determines the component of the force of gravity acting on the hoop. As the angle increases, the component of the force of gravity parallel to the incline also increases, resulting in an increase in speed. However, as the incline becomes steeper, the frictional force between the hoop and the incline also increases, causing the speed of the hoop to decrease.

What is the role of the coefficient of friction in hoop rolling down incline?

The coefficient of friction plays a significant role in hoop rolling down incline as it determines the amount of frictional force between the hoop and the inclined surface. A higher coefficient of friction means there is more resistance to the motion of the hoop, resulting in a slower speed. In contrast, a lower coefficient of friction allows the hoop to roll more easily, resulting in a higher speed.

What are some real-life applications of hoop rolling down incline?

Hoop rolling down incline has several real-life applications, such as in the design of roller coasters, where the motion of the cars is similar to a hoop rolling down an incline. It is also used in the study of rotational motion and the dynamics of objects with a circular shape. Additionally, it can be used to demonstrate the principles of energy conservation and the effects of friction on motion.

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