They are the same. If this is all happening on Earth, then the ball's acceleration is 9.8 m/s^2 in either case. That's the acceleration of gravity around here.
Answer:
0.181
Explanation:
We can convert the 0.5 rps into standard angular velocity unit rad/s knowing that each revolution is 2π:
ω = 0.5 rps = 0.5*2π = 3.14 rad/s
From here we can calculate the centripetal acceleration
Using Newton 2nd law we can calculate the centripetal force that pressing on the rider, as well as the reactive normal force:
Also the friction force and friction acceleration
For the rider to not slide down, friction acceleration must win over gravitational acceleration g = 9.81 m/s2:
Answer:
planet that is farthest away is planet X
kepler's third law
Explanation:
For this exercise we can use Kepler's third law which is an application of Newton's second law to the case of the orbits of the planets
T² = (
a³ = K_s a³
Let's apply this equation to our case
a =
for this particular exercise it is not necessary to reduce the period to seconds
Plant W
10² = K_s
a_w =
a_w =
4.64
Planet X
a_x =
a_x = \frac{1}{ \sqrt[3]{K_s} } 74.3
Planet Y
a_y =
a_y = \frac{1}{ \sqrt[3]{K_s} } 18.6
Planet z
a_z =
a_z = \frac{1}{ \sqrt[3]{K_s} } 41.8
From the previous results we see that planet that is farthest away is planet X
where we have used kepler's third law
The solution for this problem is:
500 revolution per
minute = 8.33rev /s = 2π*8.33 rad /s = 52.36 rad /s
Angular velocity ω = 2π N
Angular acceleration α= (ω2 - ω1) /t
ω2 = 0
α = - ω1/t = -2π N /t
N = 500 rpm = 8.33 r p s.
α = -2π 8.33 /2.6 =- 20 rad/s^2