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
