Answer:
The extension of the wire is 0.362 mm.
Explanation:
Given;
mass of the object, m = 4.0 kg
length of the aluminum wire, L = 2.0 m
diameter of the wire, d = 2.0 mm
radius of the wire, r = d/2 = 1.0 mm = 0.001 m
The area of the wire is given by;
A = πr²
A = π(0.001)² = 3.142 x 10⁻⁶ m²
The downward force of the object on the wire is given by;
F = mg
F = 4 x 9.8 = 39.2 N
The Young's modulus of aluminum is given by;
![Y = \frac{stress}{strain}\\\\Y = \frac{F/A}{e/L}\\\\Y = \frac{FL}{Ae} \\\\e = \frac{FL}{AY}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7Bstress%7D%7Bstrain%7D%5C%5C%5C%5CY%20%3D%20%5Cfrac%7BF%2FA%7D%7Be%2FL%7D%5C%5C%5C%5CY%20%3D%20%5Cfrac%7BFL%7D%7BAe%7D%20%5C%5C%5C%5Ce%20%3D%20%5Cfrac%7BFL%7D%7BAY%7D)
Where;
Young's modulus of elasticity of aluminum = 69 x 10⁹ N/m²
![e = \frac{FL}{AY} \\\\e = \frac{(39.2)(2)}{(3.142*10^{-6})(69*10^9)} \\\\e = 0.000362 \ m\\\\e = 0.362 \ mm](https://tex.z-dn.net/?f=e%20%3D%20%5Cfrac%7BFL%7D%7BAY%7D%20%5C%5C%5C%5Ce%20%3D%20%5Cfrac%7B%2839.2%29%282%29%7D%7B%283.142%2A10%5E%7B-6%7D%29%2869%2A10%5E9%29%7D%20%5C%5C%5C%5Ce%20%3D%200.000362%20%5C%20m%5C%5C%5C%5Ce%20%3D%200.362%20%5C%20mm)
Therefore, the extension of the wire is 0.362 mm.
Answer:
Radius of the circle will be 2.5 m
Explanation:
We have given velocity of particle moving in the circle v = 5 m/sec
Acceleration of particle in the circle ![a=10m/sec^2](https://tex.z-dn.net/?f=a%3D10m%2Fsec%5E2)
We have to find the radius of the circle
We know that acceleration is given by ![a=\frac{v^2}{r}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%5E2%7D%7Br%7D)
So ![10=\frac{5^2}{r}](https://tex.z-dn.net/?f=10%3D%5Cfrac%7B5%5E2%7D%7Br%7D)
![r=\frac{25}{10}=2.5m](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B25%7D%7B10%7D%3D2.5m)
So radius of the circle will be 2.5 m
It is same as calculating maths for math
Yes. It means that the acceleration increases at a constant rate, for example 3 mph every second.
Answer:
Electric force, ![F=-3.59\times 10^6\ N](https://tex.z-dn.net/?f=F%3D-3.59%5Ctimes%2010%5E6%5C%20N)
Explanation:
Given that,
Electric charge 1, ![q_1=+40\ C](https://tex.z-dn.net/?f=q_1%3D%2B40%5C%20C)
Electric charge 2, ![q_2=-40\ C](https://tex.z-dn.net/?f=q_2%3D-40%5C%20C)
Distance, ![d=2\ km=2\times 10^3\ m](https://tex.z-dn.net/?f=d%3D2%5C%20km%3D2%5Ctimes%2010%5E3%5C%20m)
To find,
The electric force between these two sets of charges.
Solution,
There exists a force between two electric charges and this force is called electrostatic force. It is equal to the product of electric charged divided by square of distance between them.
![F=k\dfrac{q_1q_2}{d^2}](https://tex.z-dn.net/?f=F%3Dk%5Cdfrac%7Bq_1q_2%7D%7Bd%5E2%7D)
k is the electrostatic constant
![F=8.99\times 10^9\times \dfrac{40\times (-40)}{(2\times 10^3)^2}](https://tex.z-dn.net/?f=F%3D8.99%5Ctimes%2010%5E9%5Ctimes%20%5Cdfrac%7B40%5Ctimes%20%28-40%29%7D%7B%282%5Ctimes%2010%5E3%29%5E2%7D)
![F=-3.59\times 10^6\ N](https://tex.z-dn.net/?f=F%3D-3.59%5Ctimes%2010%5E6%5C%20N)
So, the electric force between these two sets of charges is
.