A 90-g bead is attached to the end of a 60-cm length of massless string. The other end of the string is held at point O, which i
s 200 cm above the floor, and the bead is swung counterclockwise at a constant speed in a vertical circle. The tension in the string when the bead is at the very bottom of the circle is 2.2 N. While the bead is in motion, a very sharp knife is inserted to cut the string directly below point O. How far to the right of the center of the circle does the bead hit the floor?
1 answer:
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Answer:
(a). The initial velocity is 28.58m/s
(b). The speed when touching the ground is 33.3m/s.
Explanation:
The equations governing the position of the projectile are
where is the initial velocity.
(a).
When the projectile hits the 50m mark, ; therefore,
solving for we get:
Thus, the projectile must hit the 50m mark in 1.75s, and this condition demands from equation (1) that
which gives
(b).
The horizontal velocity remains unchanged just before the projectile touches the ground because gravity acts only along the vertical direction; therefore,
the vertical component of the velocity is
which gives a speed of