Help me with these four questions. midterm study. Physics12

joeseppe
I've been doing a lot of extra questions for physics lately, but I just can't wrap my head around these questions. I've attempted a a lot of others, but these just seem different for some reason? Please help me solve them, including Free Body Diagrams if possible.

1. If a curve with a radius of 60m is properly banked for a car traveling at 60km/hr, what must the coefficient of static friction be for a car not to skid when traveling at 90km/hr?

2. A satellite of mass "m" moves in a circular orbit about the Earth at a height "h" above its surface. If the radius of the Earth is R and the accel due to gravity at the Earth's surface is "g" show that the period of the satellite can be expressed as T=2pi*route((R+h)^3 / gR^2)

3. Calculate the mass of the sun using the fact that the period of the Earth is 3.16x10^7 seconds and its mean distance from the sun is 1.5x10^11m. (G=6.67x10^-11 Nm^2/kg^2)

4. Conical pendulum question-
An amusement park ride consists of a rotating circular platform 8m in diameter from which seats are suspended at the end of 2.5m chains. When the system rotates the cahins holding the seats make an angle theta=28degrees with the vertical a) what is the speed of the seat? b) If a child of mass 40kg sits in the 10kg seat, what is the tension in the chain?

Thanks huge guys, if I can see how these questions are done, i should be set for my midterm exam.

Mentor

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joeseppe
Thanks for the welcome!

I'm not really sure where to start at all on these ones, but i'll give it a shot:

1. I know i have to get the horizontal component of acceleration, and I think I have to use $$\sum$$Fr=ma but I don't know how?

2. I'm completely confused on this one as I wasn't given any numbers, and it completely throws me when I just have to work with variables.

3. First you have to get Velocity using a=4pi^2r / T^2
so therefore Accel=5.93x10^-3
After that, i know I have to use accel somehow to get mass, but I'm not sure how exactally to do that.

4. I was sick the day this was taught, and my teacher was not much of a help trying to explain how to do conical pendulum questions. I did get the notes for that day, but I still have no idea how to even start this one :(

Staff Emeritus
Homework Helper
#3:

Here are two things we know about the force exerted by the sun on the Earth:

It is gravitational.
It results in uniform circular motion (to a good approximation).

There are formulas for the force due to gravity, as well as for the force in uniform circular motion. Equate these two expressions for force and take it from there.

p.s. I'm not sure where "get Velocity using a=4pi^2r / T^2" comes from.

joeseppe
p.s. I'm not sure where "get Velocity using a=4pi^2r / T^2" comes from.

Yeah, i meant to say "get acceleration using a=4pi^2r / T^2"

joeseppe
My midterm is tomorrow guys. If you can't, or dont' want to solve the questions even after I've attempted them to the best of my ability, then can you offer any tips to completing them?

Tentothe
1. Properly banked means a car traveling at 60 km/hr will not need friction to keep it moving in a circle. The horizontal component of the normal force alone will be sufficient for the required acceleration. You can use this fact to figure out what angle the road is banked at. When the car is traveling at 90 km/hr, friction will be involved if it is to stay in a circle. You can use free-body diagrams and the angle you calculated earlier to figure out what coefficient of static friction is required.

joeseppe
1. Properly banked means a car traveling at 60 km/hr will not need friction to keep it moving in a circle. The horizontal component of the normal force alone will be sufficient for the required acceleration. You can use this fact to figure out what angle the road is banked at. When the car is traveling at 90 km/hr, friction will be involved if it is to stay in a circle. You can use free-body diagrams and the angle you calculated earlier to figure out what coefficient of static friction is required.

Oh, i missed that part! Sort of like trick wording in there! Thanks :)

Mentor
2. A satellite of mass "m" moves in a circular orbit about the Earth at a height "h" above its surface. If the radius of the Earth is R and the accel due to gravity at the Earth's surface is "g" show that the period of the satellite can be expressed as T=2pi*route((R+h)^3 / gR^2)
Hint: This is a circular motion/centripetal acceleration problem. Apply Newton's 2nd law and Newton's law of universal gravity.

3. Calculate the mass of the sun using the fact that the period of the Earth is 3.16x10^7 seconds and its mean distance from the sun is 1.5x10^11m. (G=6.67x10^-11 Nm^2/kg^2)
This can also be treated as a circular motion/centripetal acceleration problem.

4. Conical pendulum question-
An amusement park ride consists of a rotating circular platform 8m in diameter from which seats are suspended at the end of 2.5m chains. When the system rotates the cahins holding the seats make an angle theta=28degrees with the vertical a) what is the speed of the seat? b) If a child of mass 40kg sits in the 10kg seat, what is the tension in the chain?
As always, draw a free body diagram of the seat/child. Apply Newton's 2nd law to horizontal and vertical directions. Again: Circular motion/centripetal acceleration is involved.

joeseppe
Thanks guys for the help. I ended up having something similar to 1 on my test today. Number 4 was identical actually!

I nailed 1. 100%.

Number 4 I'm not so sure about. I drew a FBD, but got confused because the angle of 28 degrees was 4m out from the center of the platform. I calculated a new radius based on the 2.5m chain plus the angle of 28 degrees and added that onto the 4m radius I had to start, and used this new R for the rest of the question.

Also for the rest of the question, i found the new angle (50 something degrees if I remember correctly) between the center of the platform and the final point of the seat at the end of the 2.5m chain. Was I wrong in doing so? (and used this angle to calculate the tension)

Anyways, its over now, thanks again everyone for your help :)

Mentor
Number 4 I'm not so sure about. I drew a FBD, but got confused because the angle of 28 degrees was 4m out from the center of the platform. I calculated a new radius based on the 2.5m chain plus the angle of 28 degrees and added that onto the 4m radius I had to start, and used this new R for the rest of the question.
So far, so good.

Also for the rest of the question, i found the new angle (50 something degrees if I remember correctly) between the center of the platform and the final point of the seat at the end of the 2.5m chain. Was I wrong in doing so? (and used this angle to calculate the tension)
All you need is the angle the chain makes with the vertical, which is given. Use that to resolve the tension force into horizontal and vertical components. Then analyze vertical force components to solve for the tension.