Atetherball is tied to the end of a string of negligible mass. the ball is struck so that it moves in uniform circular motion in a horizontal plane, and the string makes an angle of 26° with the vertical pole. the mass of the ball is 1.3 kg. what is the ball's speed

v =  24sqrt{r} m/s

Explanation:

as vertical force is equal to weight,

hence W= Fc Cos 26

now ,   mass= mg

and Fc= mv^{2}/r

where r is the length of string.

putting all the values together in equation 1 :

mg = mv^{2}/r Cos 26

v^{2} = rg Cos 26

v^{2} = r (9.8) Cos 26

v^{2} = 9.8 * (.64691) r

   v =  24sqrt{r} m/s

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s