Inclined plane moment of inertia

In summary, the problem involves a block sliding down an inclined surface with a coefficient of kinetic friction and a string attached to a flywheel. The acceleration of the block down the plane and the tension in the string are calculated using the equations for forces and torque. The final answers are a = 1.123 m/s^2 and T = 14 N.
  • #1
pat666
709
0

Homework Statement



A block with mass m = 5.00 kg slides down a surface inclined 36.9 to the horizontal. The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a flywheel has mass 25.0 kg and moment of inertia 0.500 kgm2 with respect to the axis of rotation. The string pulls without slipping at a perpendicular distance of 0.200 m from that axis.
a) What is the acceleration of the block down the plane
b) What is the tension in the string

Homework Equations





The Attempt at a Solution


Ok I've been having a lot of trouble with things involving moments of inertia. I've found the friction that opposes the motion to be 9.81N. but how do i calculate the opposing force that the flywheel provides? any help is appreciated, as always..
 
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  • #2
Could you please show a picture?

ehild
 
  • #3
Could you please show a picture?

ehild
 
  • #4
How do you show a picture in a reply?? I've attached it as a word doc.
 

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  • #5
Use the relationship [tex]\alpha[/tex]=a/r and solve the torque equation for a.
 
  • #6
you mean mg-T=ma??
 
  • #7
First sum up all of the forces for the block.

[tex]\Sigma[/tex]Fx=sin[tex]\theta[/tex]*Fg-Ff-T=ma

Then get the pulley

[tex]\Sigma\tau[/tex]=I*[tex]\alpha[/tex]
 
  • #8
Ok ill do that and report back with my answer, thanks.
 
  • #9
Hey is the answer a=1.123m/s^2 and T=14N thanks
 
  • #10
Yes, it is!

ehild
 
  • #11
Hey Pat,

Could you describe what you've done to come up with those answers? I couldn't follow.

Cheers
 
  • #12
why do you want to follow, more cqu peoples?
 
Last edited:
  • #13
69camaro said:
Hey Pat,

Could you describe what you've done to come up with those answers? I couldn't follow.

Cheers

which part?
 

1. What is the definition of moment of inertia for an inclined plane?

The moment of inertia for an inclined plane is a measure of the object's resistance to rotational motion around a specific axis, taking into account the object's mass distribution and the distance from the axis of rotation.

2. How is the moment of inertia calculated for an inclined plane?

The moment of inertia for an inclined plane can be calculated by taking the sum of the mass of each infinitesimally small element multiplied by the square of its distance from the axis of rotation. This can also be expressed as the integral of the mass distribution over the entire object.

3. How does the angle of the inclined plane affect the moment of inertia?

The angle of the inclined plane affects the moment of inertia by changing the distribution of mass around the axis of rotation. As the angle increases, the distance of the mass from the axis of rotation increases, resulting in a larger moment of inertia.

4. What is the significance of the moment of inertia for an inclined plane?

The moment of inertia for an inclined plane is important in understanding the rotational motion and stability of an object on the inclined plane. It also plays a role in determining the amount of energy required to rotate the object around the axis of rotation.

5. How can the moment of inertia for an inclined plane be applied in real-life situations?

The concept of moment of inertia for an inclined plane can be applied in various real-life situations, such as designing structures that can withstand rotational forces, calculating the energy needed for objects to roll or slide down an inclined plane, and analyzing the stability of objects on an inclined surface.

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