Ciara is swinging a 0.015 kg ball tied to a string around her head in a flat, horizontal circle. the radius of the circle is 0.70 m. it takes the ball 0.60 seconds to complete one full circle. calculate the tension in the string and its direction that provides the centripetal force acting on the ball to keep it in the circular path.
a) 0.0077 n, toward the center of the circle
b) 1.2 n, toward the center of the circle
c) 0.0077 n, along the line tangent to the circle
d) 1.2 n, along the line tangent to the circle

B) 1.2 N, toward the center of the circle

Explanation:

The circumference of the circle is:

C = 2πr

C = 2π (0.70 m)

C = 4.40 m

So the velocity of the ball is:

v = C/t

v = 4.40 m / 0.60 s

v = 7.33 m/s

Sum of the forces in the radial direction:

∑F = ma

T = m v² / r

T = (0.015 kg) (7.33 m/s)² / (0.70 m)

T = 1.2 N

The tension force is 1.2 N towards the center of the circle.

1.2 N, toward the center of the circle

Explanation:

It is given that,

Mass of the ball, m = 0.015 kg

The radius of the circle, r = 0.7 m

Time taken by the ball to complete complete circle, t = 0.6 s

We need to find the tension in the string and its direction that provides the centripetal force acting on the ball to keep it in the circular path. Here, tension in the string balances the centripetal force so that the ball moves in circular path. So,

Since,

So,

T = 1.15 N

or

T = 1.2 N

The direction of centripetal force is toward the center of circle. So, the correct option is (b).

if the person is shown to have +90n, then ans is -10n.

if the person is shown to have -90n, then ans is +10n.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft