Respuesta :
Answer:
Time, t = 2.76 seconds
Explanation:
It is given that,
Mass of the bucket, m = 5.2 kg
The breaking strength of the cord, T = 70 N
Initially, the bucket is at rest, u = 0
Bucket is to raise a distance of 14 meters, d = 14 m
At equilibrium, the net force acting on the bucket is given by :
When the bucket is moving in upward direction,
[tex]T-mg=ma[/tex]
a is the acceleration of the bucket.
[tex]a=\dfrac{T-mg}{m}[/tex]
[tex]a=\dfrac{70-5.2\times 9.8}{5.2}[/tex]
[tex]a=3.66\ m/s^2[/tex]
Let t is the minimum time required to raise the bucket a vertical distance of 14.0 m without breaking the cord. Using second equation of motion as :
[tex]d=ut+\dfrac{1}{2}at^2[/tex]
[tex]d=\dfrac{1}{2}at^2[/tex]
[tex]t=\sqrt{\dfrac{2d}{a}}[/tex]
[tex]t=\sqrt{\dfrac{2\times 14}{3.66}}[/tex]
t = 2.76 seconds
So, the minimum time required to raise the bucket a vertical distance is 2.76 seconds. hence, this is the required solution.
The time required to pull the object from a height under the influence of gravity is the minimum time required. The minimum time required to raise the bucket is 2.76 sec.
What is breaking strength?
The ability of a material to sustain a tensile or pulling force is known as breaking strength. It's usually expressed in force per cross-sectional area. It comes under the property of the material.
The given data in the problem is ;
m = 5.2 kg
T = 70 N is the cord's breaking strength.
The bucket is initially at rest, with u = 0.
The bucket must lift a distance of 14 meters (d = 14 m).
The net force acting on the bucket at equilibrium is given by:
As the bucket is moving upward
[tex]{T-mg=ma}[/tex]
[tex]\rm{a= \frac{{T-mg}}{m} }[/tex]
[tex]\rm{a= \frac{{70-5.2\times9.8}}{5.2} }[/tex]
[tex]\rm{a= 3.66 m/s^2}[/tex]
From the second equation of motion
[tex]\rm{S = ut+\frac{1}{2} at^{2}}[/tex]
[tex]\rm{u=0}[/tex]
[tex]t = \sqrt{\frac{2a}{S} }[/tex]
[tex]t = \sqrt{\frac{2\times3.66}{14} }[/tex]
[tex]\rm{t = 2.76 sec}[/tex]
Hence the minimum time required to raise the bucket is 2.76 sec.
To learn more about the breaking strength refer to the link;
https://brainly.com/question/18297380
