Calculate speed of a hoop up an incline

In summary, the conversation includes a question about the speed of a hoop after it has rolled up a ramp, a list of relevant equations, and an attempt at a solution. The final calculation is done incorrectly, with the correct answer being 2.80 m/s.
  • #1
yoslick11
1
0

Homework Statement


Ok, I have attempted this problem, and believe I have the right answer. My work is not matching up though and I think I am missing something.

Question:
A hoop is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes and angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00m up the ramp?


Homework Equations


KE = 1/2*mv^2 + 1/2*I*w^2
I = mR^2


The Attempt at a Solution


This is what I got.

Total KE = 1/2*mv^2+1/2*Iw^2
substituting the I = mR^2 and w = v/R

Total KE = 1/2*m*v^2 + 1/2*(mR^2)*(v^2/R^2)
= 1/2*m*v^2 + 1/2*m*v^2
= mv^2

at 3m up on the incline

ke(bot) = pe(top)+ke(top)

m*v(initial)^2 = mgh + 1/2*m*v(final)^2
vi^2 = gh + 1/2*vf^2

vf = sqrt(2(vi^2-gh))

I believe at this point I am wanting vf = sqrt(vi^2-gh).. because the answer I believe is 2.80 m/s. sqrt(4.5^2 - (9.8*3sin25)) = 2.80 m/s

Am I looking at this correctly?

Any help would be appreciated.
 
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  • #2
You calculated that total KE for the rolling hoop is m v2, and used m v2 for ke(bot) but then you used 1/2 m v2 for ke(top)?
 

Related to Calculate speed of a hoop up an incline

1. How do you calculate the speed of a hoop rolling up an incline?

To calculate the speed of a hoop rolling up an incline, you will need to know the mass of the hoop, the angle of the incline, and the acceleration due to gravity. You can use the equation v = √(2gh sinθ) to calculate the speed, where v is the speed, g is the acceleration due to gravity (9.8 m/s²), h is the height of the incline, and θ is the angle of the incline.

2. Can the speed of a hoop rolling up an incline be greater than its initial speed?

Yes, the speed of a hoop rolling up an incline can be greater than its initial speed, as long as there is a net force acting on the hoop to increase its speed. This can be achieved by applying a force on the hoop or by choosing an incline with a steep angle.

3. How does the mass of the hoop affect its speed up an incline?

The mass of the hoop does not affect its speed up an incline, as long as the force applied to the hoop remains constant. This is because the mass of an object does not affect its acceleration due to gravity, which is the main factor in calculating the speed of the hoop up an incline.

4. Is the speed of a hoop rolling up an incline affected by friction?

Yes, the speed of a hoop rolling up an incline is affected by friction. Friction acts in the opposite direction of motion and can slow down the hoop, reducing its speed. To calculate the speed of the hoop taking into account friction, you can use the equation v = √(2gh sinθ - μkmgcosθ), where μk is the coefficient of kinetic friction between the hoop and the incline.

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

The angle of the incline affects the speed of the hoop by determining the height the hoop needs to reach and the distance it needs to travel to reach the top. A steeper incline will result in a higher speed, while a shallower incline will result in a lower speed. This is because a steeper incline has a greater vertical height, allowing for more potential energy to be converted into kinetic energy.

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