Uniform Circular Motion questions

[Morokana]

The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle (r = 11.0 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.910, and the angle in the drawing is 29.2°. How much time is required for your suitcase to go around once?

I tried using 2(pie)r/T for this one .. and i tried finding the velocity usin rg*tan29.2 ,,, wat next ?

Speedboat A negotiates a curve whose radius is 133 m. Speedboat B negotiates a curve whose radius is 209 m. Each boat experiences the same centripetal acceleration. What is the ratio vA/vB of the speeds of the boats?

Dont you just divide the 2 ?? .. to get the ratio ?

A 12.9-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 73.0 cm is between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 2.79 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm.

i cudnt find this one out .. but i have the knowns - 12.9kg .. 73 cm and 2.79 m/s

 

[anathema]

Hello, thank you for your post on the baggage carousel problem. To solve this problem, we can use the equation you mentioned, 2πr/T, where r is the radius of the circle and T is the time it takes for the suitcase to go around once. However, in this case, we do not know the value of T. We can use another equation, v = rg*tanθ, where v is the velocity of the suitcase, r is the radius, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle given (29.2°). We can rearrange this equation to solve for T: T = 2πr/v. Plugging in the values given, we get T = 2π*11/0.910*9.8*tan(29.2) = 8.69 seconds.

For the speedboat problem, you are correct that we can find the ratio of the speeds by simply dividing them. However, we can also use the equation v = √(rω), where v is the speed, r is the radius, and ω is the angular velocity. Since both boats have the same centripetal acceleration, we can set their equations equal to each other and solve for the ratio of the speeds: vA/vB = √(rAωA)/√(rBωB) = √(rA/rB) = √(133/209) = 0.797. Therefore, the ratio of the speeds is approximately 0.797.

For the monkey swinging on a vertical circle problem, we can use the equation Fc = mv^2/r to find the magnitude of the centripetal force, where Fc is the centripetal force, m is the mass of the monkey, v is the speed at the lowest point, and r is the radius of the circle. Plugging in the values given, we get Fc = (12.9 kg)*(2.79 m/s)^2/(0.73 m) = 49.81 N. To find the tension in the monkey's arm, we can use the equation Fnet = T - mg, where Fnet is the net force, T is the tension in the arm, and mg is the force due to gravity. At the lowest point, the net force is equal to the centripetal force,

 

[quicknote]

I would approach these questions by applying the principles of uniform circular motion. In the first question about the baggage carousel, I would use the equation v = rω to find the angular velocity (ω) of the suitcase, where v is the linear speed and r is the radius of the circle. Then, I would use the equation ω = √(μg*tanθ/r) to find the angular velocity, where μ is the coefficient of static friction, g is the acceleration due to gravity, and θ is the angle of the slope. Finally, I would use the equation T = 2π/ω to find the time (T) required for the suitcase to go around once.

For the second question about the speedboats, I would use the equation v = √(rω) to find the linear speed of each boat, where r is the radius and ω is the angular velocity. Then, I would simply take the ratio of the two speeds to find the ratio vA/vB.

In the third question about the swinging monkey, I would use the equation F = mω^2r to find the centripetal force acting on the monkey, where m is the mass, ω is the angular velocity, and r is the radius. Then, I would use the equation F = T - mg to find the tension (T) in the monkey's arm, where mg is the weight of the monkey. By solving these equations simultaneously, I would be able to find the magnitude of both the centripetal force and the tension in the monkey's arm.