One end of a cord is fixed and a small 0.300 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 è = 15.0°, the speed of the object is 6.20 m/s. At this instant, find each of the following.



(a) the tension in the string
T = . N

(b) the tangential and radial components of acceleration
ar = . m/s2 inward
at = . m/s2 downward tangent to the circle

(c) the total acceleration
atotal = .
Your response differs from the correct answer by more than 10%. Double check your calculations.m/s2 inward and below the cord at °

(d) Is your answer changed if the object is swinging up instead of swinging down?

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To find the answers to the given questions, we'll need to analyze the motion of the object using basic principles of circular motion. Let's go step by step:

(a) The tension in the string:
To find the tension in the string, we need to consider the forces acting on the object at the given position. At any point in the circular motion, the net force acting on the object is the centripetal force, which is directed towards the center of the circular path. In this case, the centripetal force is provided by the tension in the string. Therefore:
T = m * a_c

where T is the tension, m is the mass of the object, and a_c is the centripetal acceleration. We can find the centripetal acceleration using the formula:
a_c = v^2 / r

where v is the velocity of the object and r is the radius of the circular path. In this case, v = 6.20 m/s and r = 2.50 m. Substituting these values, we can find the centripetal acceleration. Then, we can substitute the acceleration into the tension equation to find the tension in the string.

(b) The tangential and radial components of acceleration:
To find the tangential and radial components of acceleration, we need to express the given angle and velocity components in terms of the acceleration components. The tangential component of acceleration (a_t) is directed along the tangent of the circular path, and the radial component of acceleration (a_r) is directed towards the center of the circular path. We can relate these components to the given angle by using trigonometry.

First, let's find the radial component (a_r):
a_r = a_c * cos(θ)

where θ is the given angle, in this case, 15.0°. Using this formula, we can calculate the value of a_r.

Next, let's find the tangential component (a_t):
a_t = a_c * sin(θ)

using the same formula, we can calculate the value of a_t.

(c) The total acceleration:
The total acceleration (a_total) is the vector sum of the radial and tangential components of acceleration. We can calculate it using the Pythagorean theorem:

a_total = √(a_r^2 + a_t^2)

By substituting the calculated values of a_r and a_t into this equation, we can determine the total acceleration.

(d) If the object is swinging up instead of swinging down, the direction of the velocity would change, but the magnitude of the velocity, and therefore the magnitude of the centripetal acceleration and tension, would remain the same. The only thing that would change is the sign of the tangential acceleration, which would now be directed upwards instead of downwards.