Respuesta :
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
At the lowest point, the potato's speed will be 6.714 meter per second.
The tension on the string is 8.81 N.
Given that mass of potato is 0.300 kg and height of string is 2.3 m.
Part A:
According to the Law of conservation of energy, total energy of object will remain constant or changes its form from one energy to another in an isolated system. Hence the potential energy of potato will be equal to its kinetic energy when the sting pulled taut and potato will be released.
Potential Energy = Kinetic Energy
[tex]mgh=\dfrac {1}{2} mv^2[/tex]
Where, [tex]m[/tex] is mass of potato, [tex]h[/tex] is height of string, [tex]g[/tex] is gravitational force on potato and [tex]v[/tex] is the velocity of potato.
[tex]0.300\times9.80\times2.3=\dfrac{1}{2}\times0.300\timesv^2[/tex]
[tex]v^2 = 45.08[/tex]
[tex]v=6.714\;\rm m/s[/tex]
So, at the lowest point, the potato's speed will be 6.714 meter per second.
Part B:
Tension on the string will be the total tension force on potato.
Total tension force on potato is the sum of force at its lowest point and gravitational force.
Total Tension Force = [tex]mg+ma^2[/tex]
Where [tex]a[/tex] is the acceleration of the potato at its lowest point.
Total tension Force = [tex]mg+m\dfrac{v^2}{h}[/tex]
Total Tension Force = [tex]0.300\times9.80+0.300\times\dfrac{(6.714)^2}{2.3}\\[/tex]
Total tension Force = [tex]2.94+5.87[/tex]
Total Tension Force = 8.81 N
Hence the tension on the string is 8.81 N.
For more details, follow the link given below.
https://brainly.com/question/2287912.
