Answer:
vf = 3.27[m/s]
Explanation:
In order to solve this problem we must analyze each body individually and find the respective equations. The free body diagram of each body (box and bucket) should be made, in the attached image we can see the free body diagrams and the respective equations.
With the first free body diagram, we determine that the tension T should be equal to the product of the mass of the box by the acceleration of this.
With the second free body diagram we determine another equation that relates the tension to the acceleration of the bucket and the mass of the bucket.
Then we equalize the two stress equations and we can clear the acceleration.
a = 3.58 [m/s^2]
As we know that the bucket descends 1.5 [m], this same distance is traveled by the box, as they are connected by the same rope.
![x = \frac{1}{2} *a*t^{2}\\1.5 = \frac{1}{2}*(3.58) *t^{2} \\t = 0.91 [s]](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2Aa%2At%5E%7B2%7D%5C%5C1.5%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%283.58%29%20%2At%5E%7B2%7D%20%5C%5Ct%20%3D%200.91%20%5Bs%5D)
And the speed can be calculated as follows:
![v_{f}=v_{o}+a*t\\v_{f}=0+(3.58*0.915)\\v_{f}= 3.27[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D%2Ba%2At%5C%5Cv_%7Bf%7D%3D0%2B%283.58%2A0.915%29%5C%5Cv_%7Bf%7D%3D%203.27%5Bm%2Fs%5D)
Answer:
=0.855V
Explanation:
The induced voltage can be calculated using below expression
E =B x dA/dt
Where dA/dt = area
B= magnetic field = 6.90×10-5 T.
We were given speed of 885 km/h but we will need to convert to m/s for consistency of unit
speed = 885 km/h
speed = 885 x 10^3 m/hr
speed = 885 x 10^3/60 x60 m/s
speed = 245.8 m/s
If The aircraft wing sweep out" an area
at t= 50.4seconds then we have;
dA/dt = 50.4 x 245.8
= 123388.32m^2/s
Then from the expression above
E =B x dA/dt substitute the values of each parameters, we have
E = 6.90 x 10^-5 x 12388.32 V
E =0.855V
Hence, the average induced voltage between the tips of the wings is =0.855V
If we consider Boyles law for gases, it states the following equation,
PV/T =k
where k is a constant
P-pressure, T- temperature and V -volume
the volume is constant at both situations as its a rigid tank as mentioned in the questions.
Therefore we consider Volume to be constant , then equation is
P/T = kV
kV = c (new constant)
P/T = c
P = cT
Therefore pressure is inversely proportional to temperature, whatever change in pressure would cause the same kind of change in temperature as well.
therefore when T decreases, P also decreases.
Answer is B
<span>when it returns to its original level after encountering air resistance, its kinetic energy is
decreased.
In fact, part of the energy has been dissipated due to the air resistance.
The mechanical energy of the ball as it starts the motion is:
</span>
<span>where K is the kinetic energy, and where there is no potential energy since we use the initial height of the ball as reference level.
If there is no air resistance, this total energy is conserved, therefore when the ball returns to its original height, the kinetic energy will still be 100 J. However, because of the presence of the air resistance, the total mechanical energy is not conserved, and part of the total energy of the ball has been dissipated through the air. Therefore, when the ball returns to its original level, the kinetic energy will be less than 100 J.</span>
