Question

This is the third time i'm submitting this same problem. can i please get a detailed explanation for all parts? thank you.

A certain string can withstand a maximum tension of 40N without breaking. A child ties a 0.37Kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91m, slowly increasing the speed until the spring breaks.

from the above problem, assume the child now whirls the stone tied in the same string in a horizontal circle of the same radius. the stone breaks the string at the height of 1.76m above the ground

a. Find the angle of the string with respect to the horizontal plane just before the stone breaks the string

b. estimate the magnitude of the acceleration of the stone before the stone breaks the string

c. find the distance the stone would fly before it hits the ground.

d. find the angle of the stone when it hits the ground

Answer 1

let the string makes an angle with the vertical plane,

Tcos = mg and Tsin = mv^2/ R

a) 40 cos = 0.37 (9.8)

cos = 0.091

= 84.77 degree

angle which stone makes with horizontal = 90- 84.77= 5.23 degree

b) let's find the velocity of stone

40 sin 84.77 = 0.37 (V)^2 / 0.91

v = 10 m/s apprx

a (accleration) = v^2/ r = 100/ 0.91= 107.658 m/s^2 apprx

c) horizontal component of velocity = 10 cos 5.23

time taken to cover an height of 1.76 m = sqroot ( 2 x 1.76/ 9.8) = 0.599 sec

horizontal distance covered = 10 cos 5.23 (0.599) = 5.965 m apprx

d) tan = 1.76/ 5.965= 0.295

= 16.43 degree ---------angel which stone makes with horizontal when it hits the ground

Note: If you still not clear. do leave a comment