Question

A mass of 3 kg is connected to a string of length 3.4 meters to form a yo-yo. It is swung in a vertical circle. The string breaks when the tension in the string is 89 Newtons. It happens to reach this tension on the side of the circle (halfway between the top and bottom) and the mass moves through midair at the velocity it was moving at the side when the string broke. What is the maximum vertical displacement of the mass after it breaks away from the string? Answer in meters.

Answer 1

Given ,mass =3kg

length of string , r =3.4m

Tensionin string =89 N

First find linear velocity when string broke

Since the mass at halfway between top and bottom

Tension in the string =mv² /r

Note: at bottom T =mv² /r+mg and at top T = mv²/r -mg

so

v= 10 m/s

---------------------------

So we got initial velocity

2^nd part is a projectile motion

so at max height velocity becomes zero

Use formula v² -u² =2as

0² - 10² = -2*9.81 *H

H =100/19.62

H=5.0968 m

ANSWER: Maximum Vertical Displacement = 5.1 m

-------------------