Final answer:
The speed of the rock when the string passes through the vertical position is approximately 3.84 m/s. The tension in the string when it makes an angle of 45° is approximately 1.18 N. The tension in the string as it passes through the vertical is approximately 1.18 N.
Step-by-step explanation:
Given: mass of rock (m) = 0.12 kg, length of string (L) = 0.80 m, maximum angle (θ) = 45°.
(a) To find the speed of the rock when the string passes through the vertical position, we can use the conservation of mechanical energy.
At the highest point, the rock has gravitational potential energy (mgh) and zero kinetic energy. At the lowest point, it has zero potential energy and maximum kinetic energy (1/2mv²).
Using the equation for mechanical energy: mgh = 1/2mv², we can solve for v. The height (h) can be found using the sine of the angle and the length of the string: h = L(1 - cosθ).
(b) To find the tension in the string when it makes an angle of 45°, we can use the centripetal force required for circular motion. The tension (T) is equal to the gravitational force (mg) plus the centripetal force (mv²/L).
(c) To find the tension in the string as it passes through the vertical, we can use the same centripetal force equation, but the angle is 0°.
(a) The speed of the rock when the string passes through the vertical position is approximately 3.84 m/s.
(b) The tension in the string when it makes an angle of 45° is approximately 1.18 N.
(c) The tension in the string as it passes through the vertical is approximately 1.18 N.