Answer:
(a). The speed at the moment of being thrown is 30.41 m/s.
(b). The maximum height is 47.18 m.
Explanation:
Given that,
Weight of stone = 3.00 N
Height = 15 m
Speed = 25.0 m/s
(a). We need to calculate the speed at the moment of being thrown
Using work energy theorem
![W=\dfrac{1}{2}m(v_{2}^2-v_{1}^2)](https://tex.z-dn.net/?f=W%3D%5Cdfrac%7B1%7D%7B2%7Dm%28v_%7B2%7D%5E2-v_%7B1%7D%5E2%29)
![-mg\times d=\dfrac{1}{2}m(v_{2}^2-v_{1}^2)](https://tex.z-dn.net/?f=-mg%5Ctimes%20d%3D%5Cdfrac%7B1%7D%7B2%7Dm%28v_%7B2%7D%5E2-v_%7B1%7D%5E2%29)
Put the value into the formula
![-9.8\times15=\dfrac{1}{2}\times(v_{2}^2-v_{1}^2)](https://tex.z-dn.net/?f=-9.8%5Ctimes15%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%28v_%7B2%7D%5E2-v_%7B1%7D%5E2%29)
![-2\times9.8\times15=25^2-v_{1}^2](https://tex.z-dn.net/?f=-2%5Ctimes9.8%5Ctimes15%3D25%5E2-v_%7B1%7D%5E2)
![-v_{1}^2=-300-25^2](https://tex.z-dn.net/?f=-v_%7B1%7D%5E2%3D-300-25%5E2)
![v_{1}=\sqrt{925}](https://tex.z-dn.net/?f=v_%7B1%7D%3D%5Csqrt%7B925%7D)
![v_{1}=30.41\ m/s](https://tex.z-dn.net/?f=v_%7B1%7D%3D30.41%5C%20m%2Fs)
(b). We need to calculate the maximum height
Using work energy theorem
![[tex]W=\dfrac{1}{2}mv_{2}^2-\dfrac{1}{2}mv_{1}^2](https://tex.z-dn.net/?f=%5Btex%5DW%3D%5Cdfrac%7B1%7D%7B2%7Dmv_%7B2%7D%5E2-%5Cdfrac%7B1%7D%7B2%7Dmv_%7B1%7D%5E2)
![mg\times d=\dfrac{1}{2}mv_{2}^2-\dfrac{1}{2}mv_{1}^2](https://tex.z-dn.net/?f=mg%5Ctimes%20d%3D%5Cdfrac%7B1%7D%7B2%7Dmv_%7B2%7D%5E2-%5Cdfrac%7B1%7D%7B2%7Dmv_%7B1%7D%5E2)
Here,
=0
![-(mg)\times d=\dfrac{1}{2}mv_{1}^2](https://tex.z-dn.net/?f=-%28mg%29%5Ctimes%20d%3D%5Cdfrac%7B1%7D%7B2%7Dmv_%7B1%7D%5E2)
![d=\dfrac{v_{1}^2}{2g}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7Bv_%7B1%7D%5E2%7D%7B2g%7D)
Put the value into the formula
![d=\dfrac{30.41^2}{2\times9.8}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B30.41%5E2%7D%7B2%5Ctimes9.8%7D)
![d=47.18\ m](https://tex.z-dn.net/?f=d%3D47.18%5C%20m)
Hence, (a). The speed at the moment of being thrown is 30.41 m/s.
(b). The maximum height is 47.18 m.
Answer: 13.1 μH
Explanation:
Given
length of heating coil, l = 1 m
Diameter of heating coil, d = 0.8 cm = 8*10^-3 m
No of loops, N = 400
L = μN²A / l
where
μ = 4π*10^-7 = 1.26*10^-6 T
A = πd²/4 = (π * .008 * .008) / 4 = 6.4*10^-5 m²
L = μN²A / l
L = [1.26*10^-6 * 400 * 400* 6.5*10^-5] / 1
L = 1.26*10^-6 * 1.6*10^5 * 6.5*10^-5
L = 1.31*10^-5
L = 13.1 μH
Thus, from the calculations above, we can say that the total self inductance of the solenoid is 13.1 μH
6 mph/s
Calculating acceleration involves dividing velocity by time — or in terms of SI units, dividing the meter per second [m/s] by the second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus the SI unit of acceleration is the meter per second squared .
The change in the player's internal energy is -491.6 kJ. The number of nutritional calories is -117.44 kCal
For this process to take place, some of the basketball player's perspiration must escape from the skin. This is because sweating relies on a physical phenomenon known as the heat of vaporization.
The heat of vaporization refers to the amount of heat required to convert 1g of a liquid into a vapor without causing the liquid's temperature to increase.
From the given information,
- the work done on the basketball is dW = 2.43 × 10⁵ J
The amount of heat loss is represented by dQ.
where;
∴
Using the first law of thermodynamics:b
dU = dQ - dW
dU = -mL - dW
dU = -(0.110 kg × 2.26 × 10⁶ J/kg - 2.43 × 10⁵ J)
dU = -491.6 × 10³ J
dU = -491.6 kJ
The number of nutritional calories the player has converted to work and heat can be determined by using the relation:
![\mathbf{dU = -491.6 \ kJ \times (\dfrac{1 \ cal}{ 4.186 \ J})}](https://tex.z-dn.net/?f=%5Cmathbf%7BdU%20%3D%20-491.6%20%5C%20kJ%20%5Ctimes%20%28%5Cdfrac%7B1%20%5C%20cal%7D%7B%204.186%20%5C%20J%7D%29%7D)
dU = -117.44 kcal
Learn more about first law of thermodynamics here:
brainly.com/question/3808473?referrer=searchResults