Question

A ball on the end of a string is whirled around in a horizontal circle of radius 0.300 m. The plane of the circle is 1.50 m above the ground. The string breaks and the ball lands 2.10 m (horizontally) away from the point on the ground directly beneath the ball's location when the string breaks. Find the radial acceleration of the ball during its circular motion. Magnitude

Answer 1

48.13 m/s²

Step-by-step explanation:

In this question, circular motion of the ball attached to string turns into trajectory motion.

Radial acceleration = (v²/r)

But we need to find the velocity, v, from the ball's trajectory motion after the string breaks.

For trajectory motion,

Range = (initial horizontal velocity) × (time of flight) = (v)(T)

v = (Range)/T

But time of flight is related to the vertical height, H, at which the trajectory motion starts through the relation,

T = √(2H/g) = √(2×1.2/9.8) = 0.553 s

v = (Range)/T

v = 2.1/0.553

v = 3.80 m/s

Radial acceleration = (v²/r) = (3.8²/0.3)

a = 48.13 m/s²