What is the force causing the sphere to roll down the ramp?

In summary, a 320 N sphere with a radius of 0.20 m rolls without slipping down a 25° inclined ramp for 6.0 m. The angular speed of the sphere at the bottom of the ramp, starting from rest, can be found using the equation F∆x=(1/2)*[(2/5)mr^2]ωf^2, since at the top it only has potential energy and at the bottom it has only kinetic energy. The mass of the sphere is not needed in this calculation.
  • #1
Dr_bug
17
0

Homework Statement



A 320 N sphere 0.20 m in radius rolls, without slipping, 6.0 m down a ramp that is inclined at 25° with the horizontal. What is the angular speed of the sphere at the bottom of the hill if it starts from rest?

Homework Equations


I sphere= (2/5)mr^2
atan=rα
v=rω

The Attempt at a Solution


I tried first to use F∆x=(1/2)*[(2/5)mr^2]ωf^2-0(zero because it starts from rest) but then i realize i don't have a mass and now i don't really know what to do. any helpful hints or suggestions would be appreicated
 
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  • #2
At the top, it only has potential energy mgh. At the bottom, the energy is entirely kinetic. Do you see why you don't need the mass?
 
  • #3
so then can i just solve the eqn i was using and just ignore m?
 
  • #4
Dr_bug said:
so then can i just solve the eqn i was using and just ignore m?

No your equation is correct. Just what is the force F in [itex]F\Delta x[/itex]?
 

FAQ: What is the force causing the sphere to roll down the ramp?

1. What is angular speed?

Angular speed, also known as rotational speed, is the rate at which an object rotates about its axis. It is measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular speed different from linear speed?

Angular speed measures how fast an object is rotating, while linear speed measures how fast an object is moving in a straight line. Angular speed is dependent on the distance from the axis of rotation, while linear speed is not.

3. How is angular speed calculated?

Angular speed is calculated by dividing the angle through which an object rotates by the time it takes to rotate through that angle. It can be represented by the formula: ω = Δθ/Δt, where ω is angular speed, Δθ is the change in angle, and Δt is the change in time.

4. What factors can affect angular speed?

Angular speed can be affected by the size and shape of the object, as well as the force and torque applied to it. Friction, air resistance, and other external forces can also impact the angular speed of an object.

5. How is angular speed used in real life?

Angular speed is used in many real-life applications, such as the rotation of wheels in vehicles, the movement of gears in machines, and the spinning of objects in sports like figure skating and gymnastics. It is also important in understanding the motion of planets and galaxies in space.

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