One end of a cord is fixed and a small 0.270-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m, as shown in the figure below. When θ = 18.0°, the speed of the object is 6.80 m/s.

(a) At this instant, find the tension in the string.
(b) At this instant, find the tangential and radial components of acceleration.
(c) At this instant, find the total acceleration.
(d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? Yes/No
(e) Explain your answer to part (d).

I got 21.14 N for (a) and 18.50 m/s^2 for the radial/centripetal acceleration in (b). I just don't know how to figure out the tangential acceleration. If I could get that, I can solve (c) also. Please help!

It's actually 7.643 N for (a) and 18.5 m/s^2 for centripetal acceleration in (b). Please help with the 2nd part!

To find the tangential acceleration in part (b) and consequently solve part (c), we need to use the given information about the speed of the object and the angle θ.

The tangential acceleration is the component of acceleration that is tangent to the circular path of the object's motion. It is responsible for changing the object's speed.

To find the tangential acceleration, we can use the equation for centripetal acceleration:

a_c = v^2 / r

where a_c is the centripetal acceleration, v is the object's speed, and r is the radius of the circle.

We are given the speed of the object (v = 6.80 m/s) and the radius of the circle (r = 2.50 m). Plugging these values into the equation, we can calculate the centripetal acceleration:

a_c = (6.80 m/s)^2 / 2.50 m = 18.464 m/s^2

This is the magnitude of the centripetal acceleration. Since the centripetal acceleration is always directed toward the center of the circle, the tangential acceleration will have the same magnitude but opposite direction.

Therefore, the tangential acceleration is:

a_t = -18.464 m/s^2

Now that we have the tangential acceleration, we can solve part (c) to find the total acceleration.

The total acceleration, a_total, is the vector sum of the radial (centripetal) acceleration and the tangential acceleration. Since the tangential acceleration has a negative sign, it will be subtracted from the radial acceleration to get the total acceleration.

a_total = a_c + a_t = 18.464 m/s^2 - 18.464 m/s^2 = 0 m/s^2

So, the total acceleration at this instant is 0 m/s^2.

Moving on to part (d), the answer does not change if the object is swinging down toward its lowest point instead of swinging up. The tension in the string, the tangential and radial accelerations, and the total acceleration would all have the same magnitudes as the object swings down. However, the directions of the tangential and radial accelerations would be different due to the change in the direction of motion.

In the case of swinging down, the tangential acceleration would be positive and in the same direction as the object's motion, while the radial acceleration would still be directed toward the center of the circular path. The total acceleration would be the vector sum of these two components, resulting in a non-zero value.

Therefore, the answer is 'No', the answer does not change if the object is swinging down toward its lowest point instead of swinging up.

I hope this explanation clarifies the remaining parts of the problem.