Answer:
Part a)
![EMF = 14 \times 10^{-3} V](https://tex.z-dn.net/?f=EMF%20%3D%2014%20%5Ctimes%2010%5E%7B-3%7D%20V)
Part b)
![EMF = 15.67 \times 10^{-3} V](https://tex.z-dn.net/?f=EMF%20%3D%2015.67%20%5Ctimes%2010%5E%7B-3%7D%20V)
Explanation:
As we know that magnetic flux through the loop is given as
![\phi = B.A](https://tex.z-dn.net/?f=%5Cphi%20%3D%20B.A)
now we have
![\phi = B\pi r^2](https://tex.z-dn.net/?f=%5Cphi%20%3D%20B%5Cpi%20r%5E2)
now rate of change in flux is given as
![\frac{d\phi}{dt} = B(2\pi r)\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5Cphi%7D%7Bdt%7D%20%3D%20B%282%5Cpi%20r%29%5Cfrac%7Bdr%7D%7Bdt%7D)
now we know that
![A = \pi r^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20r%5E2)
![0.285 = \pi r^2](https://tex.z-dn.net/?f=0.285%20%3D%20%5Cpi%20r%5E2)
![r = 0.30 m](https://tex.z-dn.net/?f=r%20%3D%200.30%20m)
Now plug in all data
![EMF = (0.20)\times 2\pi\times (0.30) \times (0.037)](https://tex.z-dn.net/?f=EMF%20%3D%20%280.20%29%5Ctimes%202%5Cpi%5Ctimes%20%280.30%29%20%5Ctimes%20%280.037%29)
![EMF = 14 \times 10^{-3} V](https://tex.z-dn.net/?f=EMF%20%3D%2014%20%5Ctimes%2010%5E%7B-3%7D%20V)
Part b)
Now the radius of the loop after t = 1 s
![r_1 = r_0 + \frac{dr}{dt}](https://tex.z-dn.net/?f=r_1%20%3D%20r_0%20%2B%20%5Cfrac%7Bdr%7D%7Bdt%7D)
![r_1 = 0.30 + 0.037](https://tex.z-dn.net/?f=r_1%20%3D%200.30%20%2B%200.037)
![r_1 = 0.337 m](https://tex.z-dn.net/?f=r_1%20%3D%200.337%20m)
Now plug in data in above equation
![EMF = (0.20)\times 2\pi\times (0.337) \times (0.037)](https://tex.z-dn.net/?f=EMF%20%3D%20%280.20%29%5Ctimes%202%5Cpi%5Ctimes%20%280.337%29%20%5Ctimes%20%280.037%29)
![EMF = 15.67 \times 10^{-3} V](https://tex.z-dn.net/?f=EMF%20%3D%2015.67%20%5Ctimes%2010%5E%7B-3%7D%20V)
Answer:
3.38 m/s
Explanation:
Mass of child = m₁ = 25
Initial speed of child = u₁ = 5 m/s
Initial speed of cart = u₂ = 0 m/s
Mass of cart = m₂ = 12 kg
Velocity of cart with child on top = v
This is a case of perfectly inelastic collision
![m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\frac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\frac{25\times 5+12\times 0}{25+12}\\\Rightarrow v=\frac{125}{37}\\\Rightarrow v=3.38\ m/s](https://tex.z-dn.net/?f=m_1u_1%2Bm_2u_2%3D%28m_1%2Bm_2%29v%5C%5C%5CRightarrow%20v%3D%5Cfrac%7Bm_1u_1%2Bm_2u_2%7D%7Bm_1%2Bm_2%7D%5C%5C%5CRightarrow%20v%3D%5Cfrac%7B25%5Ctimes%205%2B12%5Ctimes%200%7D%7B25%2B12%7D%5C%5C%5CRightarrow%20v%3D%5Cfrac%7B125%7D%7B37%7D%5C%5C%5CRightarrow%20v%3D3.38%5C%20m%2Fs)
Velocity of cart with child on top is 3.38 m/s
Answer:
F = 196 N
Explanation:
For this exercise we will use Newton's second law, we define a reference system with the x axis in the direction of movement of the stones and the y axis vertically
Y axis
N- W = 0
N = mg
X axis
F -fr = ma
In this case, they ask us for the force to keep moving, so the stones go at constant speed, which implies that the acceleration is zero.
F- fr = 0
F = fr
the friction force has the equation
fr = μ N
fr = μ mg
we substitute
F = μ mg
let's calculate
F = 0.80 9.8 25
F = 196 N
Answer:
Explanation:
let force exerted by engine be F.Net force =( F-400)N, applying newton law
F-400 = 1.5 x 10³x18 =27000 ,
F = 27400 N.
velocity after 12 s = 0 + 18 x 12 = 216 m/s
Average velocity = (0 + 216 )/2 = 108 m/s
Average power = force x average velocity = 27400 x 108 = 29.6 10⁵ W .⁶
b) At 12 s , velocity = 216 m/s
Instantaneous power = velocity x force = 216 x 27400 = 59.2 x 10⁶ W.
The equation for percent error is
% Error =
![100*|Experimental-Theoretical|/Theoretical](https://tex.z-dn.net/?f=100%2A%7CExperimental-Theoretical%7C%2FTheoretical)
Our experimental is 2.85g/cm^3 and the accepted is 2.7g/cm^3
Thus our % Error = 5.555%