Answer:
30 V
Explanation:
Given that:
The uniform electric field = 50 N/C
Voltage = 80 V
distance = 1.0 m
The potential difference of the electric field = Δ V
E_d = V₁ - V₂
50 × 1 = 80V - V₂
50 - 80 V = - V₂
-30 V = - V₂
V₂ = 30 V
Answer:
If the temperature of the air in the balloon is less than the temperature of the air surrounding the balloon then the balloon will appear slightly deflated because of the difference in temperature.
As the temperature of the air in the balloon reaches the surrounding air temperature, then the balloon will appear to be fully inflated because the temperature of the air in the balloon is the same as the surrounding air temperature.
Before the engines fail
, the rocket's horizontal and vertical position in the air are
![x=\left(103\,\frac{\rm m}{\rm s}\right)\cos53.0^\circ\,t+\dfrac12\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\cos53.0^\circ t^2](https://tex.z-dn.net/?f=x%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%5C%2Ct%2B%5Cdfrac12%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%20t%5E2)
![y=\left(103\,\frac{\rm m}{\rm s}\right)\sin53.0^\circ\,t+\dfrac12\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\sin53.0^\circ t^2](https://tex.z-dn.net/?f=y%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Csin53.0%5E%5Ccirc%5C%2Ct%2B%5Cdfrac12%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Csin53.0%5E%5Ccirc%20t%5E2)
and its velocity vector has components
![v_x=\left(103\,\frac{\rm m}{\rm s}\right)\cos53.0^\circ+\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\cos53.0^\circ t](https://tex.z-dn.net/?f=v_x%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%2B%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Ccos53.0%5E%5Ccirc%20t)
![v_y=\left(103\,\frac{\rm m}{\rm s}\right)\sin53.0^\circ+\left(32.0\,\frac{\rm m}{\mathrm s^2}\right)\sin53.0^\circ t](https://tex.z-dn.net/?f=v_y%3D%5Cleft%28103%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%5Csin53.0%5E%5Ccirc%2B%5Cleft%2832.0%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5Csin53.0%5E%5Ccirc%20t)
After
, its position is
![x=273\,\rm m](https://tex.z-dn.net/?f=x%3D273%5C%2C%5Crm%20m)
![y=362\,\rm m](https://tex.z-dn.net/?f=y%3D362%5C%2C%5Crm%20m)
and the rocket's velocity vector has horizontal and vertical components
![v_x=120\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_x%3D120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
![v_y=159\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_y%3D159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
After the engine failure
, the rocket is in freefall and its position is given by
![x=273\,\mathrm m+\left(120\,\frac{\rm m}{\rm s}\right)t](https://tex.z-dn.net/?f=x%3D273%5C%2C%5Cmathrm%20m%2B%5Cleft%28120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t)
![y=362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)t-\dfrac g2t^2](https://tex.z-dn.net/?f=y%3D362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t-%5Cdfrac%20g2t%5E2)
and its velocity vector's components are
![v_x=120\,\frac{\rm m}{\rm s}](https://tex.z-dn.net/?f=v_x%3D120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D)
![v_y=159\,\frac{\rm m}{\rm s}-gt](https://tex.z-dn.net/?f=v_y%3D159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D-gt)
where we take
.
a. The maximum altitude occurs at the point during which
:
![159\,\frac{\rm m}{\rm s}-gt=0\implies t=16.2\,\rm s](https://tex.z-dn.net/?f=159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D-gt%3D0%5Cimplies%20t%3D16.2%5C%2C%5Crm%20s)
At this point, the rocket has an altitude of
![362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)(16.2\,\rm s)-\dfrac g2(16.2\,\rm s)^2=1650\,\rm m](https://tex.z-dn.net/?f=362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%2816.2%5C%2C%5Crm%20s%29-%5Cdfrac%20g2%2816.2%5C%2C%5Crm%20s%29%5E2%3D1650%5C%2C%5Crm%20m)
b. The rocket will eventually fall to the ground at some point after its engines fail. We solve
for
, then add 3 seconds to this time:
![362\,\mathrm m+\left(159\,\frac{\rm m}{\rm s}\right)t-\dfrac g2t^2=0\implies t=34.6\,\rm s](https://tex.z-dn.net/?f=362%5C%2C%5Cmathrm%20m%2B%5Cleft%28159%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29t-%5Cdfrac%20g2t%5E2%3D0%5Cimplies%20t%3D34.6%5C%2C%5Crm%20s)
So the rocket stays in the air for a total of
.
c. After the engine failure, the rocket traveled for about 34.6 seconds, so we evalute
for this time
:
![273\,\mathrm m+\left(120\,\frac{\rm m}{\rm s}\right)(34.6\,\rm s)=4410\,\rm m](https://tex.z-dn.net/?f=273%5C%2C%5Cmathrm%20m%2B%5Cleft%28120%5C%2C%5Cfrac%7B%5Crm%20m%7D%7B%5Crm%20s%7D%5Cright%29%2834.6%5C%2C%5Crm%20s%29%3D4410%5C%2C%5Crm%20m)
Answer:
1.6 s
Explanation:
To find the time in which the potential difference of the inductor reaches 24V you use the following formula:
![V_L=V_oe^{-\frac{Rt}{L}}](https://tex.z-dn.net/?f=V_L%3DV_oe%5E%7B-%5Cfrac%7BRt%7D%7BL%7D%7D)
V_o: initial voltage = 60V
R: resistance = 24-Ω
L: inductance = 42H
V_L: final voltage = 24 V
You first use properties of the logarithms to get time t, next, replace the values of the parameter:
![\frac{V_L}{V_o}=e^{-\frac{Rt}{L}}\\\\ln(\frac{V_L}{V_o})=-\frac{Rt}{L}\\\\t=-\frac{L}{R}ln(\frac{V_L}{V_o})\\\\t=-\frac{42H}{24\Omega}ln(\frac{24V}{60V})=1.6s](https://tex.z-dn.net/?f=%5Cfrac%7BV_L%7D%7BV_o%7D%3De%5E%7B-%5Cfrac%7BRt%7D%7BL%7D%7D%5C%5C%5C%5Cln%28%5Cfrac%7BV_L%7D%7BV_o%7D%29%3D-%5Cfrac%7BRt%7D%7BL%7D%5C%5C%5C%5Ct%3D-%5Cfrac%7BL%7D%7BR%7Dln%28%5Cfrac%7BV_L%7D%7BV_o%7D%29%5C%5C%5C%5Ct%3D-%5Cfrac%7B42H%7D%7B24%5COmega%7Dln%28%5Cfrac%7B24V%7D%7B60V%7D%29%3D1.6s)
hence, after 1.6s the inductor will have a potential difference of 24V
Answer:
The electric field strength at the midpoint of the line joining the charges is zero (0)
Explanation:
Given that the two charges are both positive (same charge) and are equal in magnitude that is 6uC. The electric field strength at the midpoint of the line joining the two charges will be equal and opposite in magnitude, therefore they will cancel each other out and the electric field strength at this point will be equal to zero.