Question

A 0.300 kg potato is tied to a string with length 2.30 m , and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of support, with the string pulled taut, and is then released.
Part A) What is the speed of the potato at the lowest point of its motion? let g be = 9.80 m/s^2
Part B) What is the tension on the string at this point?

Answer 1

Answer:

The speed of the potato at the lowest point is 6.714 m/s

The tension in the string is 8.82 N

Explanation:

We will use law of conservation of energy to find out the velocity

When the potato is at 2.30 m height, it will have potential energy and when  the potato released it will go lowest point and it's potential energy will be convert into kinetic energy.

                       Potential energy = Kinetic energy

                                  m×g×h      = (1/2) m×v²

m stands  for mass

g stands for gravitational constant

h stands for height

v stands for velocity

                      m×g×h      = (1/2) m×v²

                      0.3×9.8×2.3 = (1/2) .3×v²

                       v² = 45.08

                       v  = 6.714 m/s

The speed of the potato at lowest point is 6.714 m/s

Part B

 The potato is in uniform circular motion so the acceleration is given by

                          a = v² / r

a stands for centripetal acceleration

According to Newton second law the acceleration  is  directly proportional to applied force and inversely proportional to the mass of object

     So                     ∑ F = m × a

Two forces act on potato 1. weight due to gravitation in downward direction 2. tension in upward direction So the above equation become

                     Tension force - Force due to weight = m×a

                     T-m×g     = m×a

           centripetal acceleration formula =v²/r    ,   r = l = length of the string

                        T  = m ×(v²/l) + m×g

  v = 6.714 m/s ,  l = 2.30 m ,   m = .3 kg Now put values in above equation

                         T = .3 × (6.714²/2.30) + .3 × 9.8

                        T  = .3 ( 45.08/2.30) + 2.94

                        T  = .3 (19.6) +2.94

                        T  = 5.88 + 2.94

                        T  = 8.82 N

          The tension in the string is 8.82 N