Two dimensional movements and circular motion

[karljohan]

Homework Statement

Hello, i got three different assignments i need help with right now, my teacher overestimated me and my physics skills, so I'm kind of lost on these three:

(i'm european so i work with meters)
1:
A planets radius is 10 000 km. the gravitationalacceleration is g0 = 15 m/s^2 on the planets poles.
The gravitationalacceleration on the equator is ge = 0 m/s^2

How fast does the planet rotate?

2:
A cyclist is riding his bike in a circle, his speed is v = 72 km/h and the radius of the circle is r = 25 m
what's the angle alpha?

http://sv.tinypic.com/view.php?pic=xgjqef&s=8#.Vhp9zytbfo0

3:
a piece of garbage is hanging from a line. the mass of the garbage is m = 20 kg
The line forms the angle alpha = 5 degress (watch my picture) the the tension of the line?
http://sv.tinypic.com/view.php?pic=14l5ra&s=8#.Vhp_MStbfo0

The Attempt at a Solution

1: I'm clueless.
2: clueless
3: I'm thinking of dividing the counter force into two vectors, one vertical and one horizontal. and then somehow achieve an answer.

I'm on thin ice please help godsspeed.

 

[paisiello2]

For 1. and 2. have you studied centrifugal force in your class?

For 3. you are on the right track, can you continue with an attempt?

 

[karljohan]

Yes, i have studied centrifugal force in my class, but I'm not very good at it, and need help.

i will make an attempt at question 3:

http://sv.tinypic.com/view.php?pic=5ofitg&s=8#.Vhqp3ytbfo0

L = R

L + R = 9.82 * 20 = 196.4 N

L = R = 196.4 N / 2 = 98.2 N

sin 5 = Fy / 98.2 N => Fy = 98.2 * sin 5 = 8.55 N

cos 32 = Fx / 98.2 N => Fx = 98.2 N * cos 5 = 97.8 N

 

[SteamKing]

In the future, please post one problem per thread. PF doesn't put a limit on the number of threads you can create, and having one problem in each thread helps you keep the replies pertinent to that problem.

 

[SteamKing]

Yes, i have studied centrifugal force in my class, but I'm not very good at it, and need help.

i will make an attempt at question 3:

http://sv.tinypic.com/view.php?pic=5ofitg&s=8#.Vhqp3ytbfo0

L = R

L + R = 9.82 * 20 = 196.4 N

L = R = 196.4 N / 2 = 98.2 N

sin 5 = Fy / 98.2 N => Fy = 98.2 * sin 5 = 8.55 N

cos 32 = Fx / 98.2 N => Fx = 98.2 N * cos 5 = 97.8 N

You should draw a force triangle here. The unknown force in the line is the hypotenuse of the triangle, and you have calculated the vertical force due to the weight of the garbage bag, and the included angle is 5°. Check your trigonometry.

 

[karljohan]

[PLAIN]https://upload.wikimedia.org/math/5/4/d/54dbac66cd66b9ddaf8d9cbc760adf03.png97.8^2 + 8.55^2 = L = R

L = R = 98.17

can't be right