Determine the angle between the inclined plane and the horizontal

Also, there is no "final" in this paragraph.In summary, the conversation discussed the motion of a hollow cylinder and solid sphere down an inclined plane, using equations for displacement and moment of inertia to determine the angle of the plane. It also estimated the period of rotation of the sun if it were to collapse into a neutron star. Finally, it applied the principle of conservation of angular momentum to determine the final angular velocity of a system of masses rotating around a central post. However, further information is needed to fully understand and confirm the calculations.
  • #1
Gtseviper
A hollow, thin-walled cylinder and a solid sphere start from rest and roll without slipping down an inclined plane of length 5 m. The cylinder arrives at the bottom of the plane 2.6 s after the sphere. Determine the angle between the inclined plane and the horizontal.

x=Vo + 1/2 at^2 and I got 3.97s for t
I=1/2 M(R^2 + R^2 I=2/5 MR^2
I got 5.20 for phida

The sun's radius is 6.96 108 m, and it rotates with a period of 25.3 days. Estimate the new period of rotation of the sun if it collapses with no loss of mass to become a neutron star of radius 5.3 km.

T2/T1 = R^2/R^2 and I got 1.47 x 10^-9 days m for T2 and then I converted it and get 1.27 x 10^-4ms
Figure 10-45 shows a hollow cylindrical tube of mass M = 0.8 kg and length L = 1.9 m. Inside the cylinder are two masses m = 0.4 kg, separated a distance = 0.6 m and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. The system rotates at such that the tension in the string is 108 N just before it breaks.

M xWo^2 x r=T to get 30 rad/s for Wo
I initial=ML^2/10 + mr^2 +mr^2 and I got 1.01 kg m^2
I final=ML^2/10 +Mr^2 +Mr^2 and I got 2.96 kg m^2
Io Wo= I(final) W(final) and I got 10.25 rad/s for W(final)
 

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  • #2
x=Vo + 1/2 at^2 and I got 3.97s for t
I=1/2 M(R^2 + R^2 I=2/5 MR^2
For which? The cylinder or the sphere?
I got 5.20 for phida
I have no idea if this is right or wrong. You didn't say what
"phida" means.

The sun's radius is 6.96 108 m, and it rotates with a period of 25.3 days. Estimate the new period of rotation of the sun if it collapses with no loss of mass to become a neutron star of radius 5.3 km.

T2/T1 = R^2/R^2 and I got 1.47 x 10^-9 days m for T2 and then I converted it and get 1.27 x 10^-4ms
Okay, you used "conservation of angular momentum". Looks good.

Figure 10-45 shows a hollow cylindrical tube of mass M = 0.8 kg and length L = 1.9 m. Inside the cylinder are two masses m = 0.4 kg, separated a distance = 0.6 m and tied to a central post by a thin string. The system can rotate about a vertical axis through the center of the cylinder. The system rotates at such that the tension in the string is 108 N just before it breaks.
What is the question? In any case, you don't say what the radius of the cylinder is.
 
  • #3



The angle between the inclined plane and the horizontal can be determined using the given information. We know that the cylinder and sphere start from rest and roll without slipping, and the cylinder arrives at the bottom of the plane 2.6 seconds after the sphere. Using the equation x = Vo + 1/2 at^2, we can calculate the time it takes for the cylinder to reach the bottom of the plane, which is 3.97 seconds.

Next, we can use the moment of inertia formula I = 1/2MR^2 + 2/5MR^2 to calculate the moment of inertia for both the cylinder and sphere. Plugging in the given masses and radii, we get a moment of inertia of 5.20 for the cylinder.

Using the equation T2/T1 = R2/R1, we can calculate the new period of rotation for the sun if it were to collapse into a neutron star with a radius of 5.3 km. This gives us a new period of rotation of approximately 1.27 x 10^-4 milliseconds.

Lastly, for the system of the hollow cylindrical tube and two masses, we are given that the tension in the string is 108 N just before it breaks and the system is rotating at an angular velocity of 30 rad/s. Using the equation M x Wo^2 x r = T, we can calculate the moment of inertia for the system to be 1.01 kg m^2. Once the string breaks, the masses will move further away from the center, increasing the moment of inertia to 2.96 kg m^2. Using the equation Io x Wo = I(final) x W(final), we can solve for the final angular velocity, which comes out to be 10.25 rad/s.
 

1. What is an inclined plane?

An inclined plane is a flat surface that is at an angle to the horizontal plane, often used to make it easier to lift or move objects.

2. How do you determine the angle between an inclined plane and the horizontal?

To determine the angle, you can use a protractor or a clinometer to measure the angle between the horizontal ground and the inclined surface.

3. Can the angle between an inclined plane and the horizontal change?

Yes, the angle can change depending on the height and length of the inclined plane, as well as the weight and position of the object on the inclined plane.

4. What is the relationship between the angle of the inclined plane and the effort required to lift an object?

The smaller the angle of the inclined plane, the less effort is required to lift an object. This is because the inclined plane reduces the effective weight of the object by spreading it over a larger distance.

5. How is the angle of an inclined plane used in everyday life?

Inclined planes are used in many everyday objects and activities, such as ramps, stairs, and even playground slides. They are also used in machines like wheelchairs and cars to make it easier to move objects or people up and down.

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