Explanation:
Given that,
Length of the cable is 19.6 m, l = 19.6 m
Let us assume that the angle with vertical rotating pole is 62.5 degrees.
The total mass of a chair and its occupant is 250 kg.
(a) Let T is the tension in the cable attached to the chair. So,
[tex]T\cos\theta=mg\\\\T=\dfrac{mg}{\cos\theta}\\\\T=\dfrac{250\times 9.8}{\cos(62.5)}\\\\T=5305.91\ N[/tex]
(b) The centripetal acceleration is balanced by :
[tex]\dfrac{v^2}{r}=g\tan\theta\\\\v=\sqrt{Rg\tan\theta} \\\\v=\sqrt{l\sin\theta g\tan\theta}\\\\v=\sqrt{19.6\times \sin(62.5)9.8\times \tan(62.5)}\\\\v=18.09\ m/s[/tex]
Hence, this is the required solution.
Answer:
Explanation:
radius, R = 19.6 m
mass, m = 250 kg
(a) The tension in the cable is T.
T = mg
T = 250 x 9.8
T = 2450 N
(b) Let v is the speed of the chair.
the tension force is balanced by the centripetal force.
T = mv²/r
2450 = 250 x v²/19.6
v² = 192.08
v = 13.86 m/s
Thus, the speed of the car is 13.86 m/s
