Solution :
Given data :
Mass of the merry-go-round, m= 1640 kg
Radius of the merry-go-round, r = 7.50 m
Angular speed, 
rev/sec
rad/sec
= 5.89 rad/sec
Therefore, force required,
= 427126.9 N
Thus, the net work done for the acceleration is given by :
W = F x r
= 427126.9 x 7.5
= 3,203,451.75 J
(a) The net flux through the coil is zero.
In fact, the magnetic field generated by the wire forms concentric circles around the wire. The wire is placed along the diameter of the coil, so we can imagine as it divides the coil into two emisphere. Therefore, the magnetic field of the wire is perpendicular to the plane of the coil, but the direction of the field is opposite in the two emispheres. Since the two emispheres have same area, then the magnetic fluxes in the two emispheres are equal but opposite in sign, and so they cancel out when summing them together to find the net flux.
(b) If the wire passes through the center of the coil but it is perpendicular to the plane of the wire, the net flux through the coil is still zero.
In fact, the magnetic field generated by the wire forms concentric lines around the wire, so it is parallel to the plane of the coil. But the flux is equal to
where
is the angle between the direction of the magnetic field and the perpendicular to the plane of the coil, so in this case
and so the cosine is zero, therefore the net flux is zero.
Answer:
Relative to the ground, the velocity of the aircraft is 240 km/hr
Explanation:
Relative velocity is different from normal velocity;
When 2 objects are moving in opposite directions towards each other, they will appear to be faster than they actually are;
This is known as the relative velocity;
The information tells us we have the aircraft moving 320 km/hr northwards relative to the wind;
The wind is in the opposite direction at 80 km/hr;
R = relative velocity of the aircraft
v = actual velocity of the aircraft
w = velocity of the wind
R = v + w
Note: if the wind was moving in the same direction, the formula would be R = v - w
320 = v + 80
v = 320 - 80
v = 240
The velocity relative to the ground is simply the actual velocity as the ground doesn't move;
So, relative to the ground, the velocity of the aircraft is simply 240 km/hr
Answer:
a) 2.87 m/s
b) 3.23 m/s
Explanation:
The avergare velocity can be found dividing the length traveled d by the total time t.
a)
For the first part we easily know the total traveled length which is:
d = 50.2 m + 50.2 m = 100.4 m
The time can be found dividing the distance by the velocity:
t1 = 50.2 m / 2.21 m/s = 22.7149 s
t2 = 50.2 m / 4.11 m/s = 12.2141 s
t = t1 +t2 = 34.9290 s
Therefore, the average velocity is:
v = d/t =2.87 m/s
b)
Here we can easily know the total time:
t = 1 min + 1.16 min = 129.6 s
Now the distance wil be found multiplying each velocity by the time it has travelled:
d1 = 2.21 m/s * 60 s = 132.6 m
d2 = 4.11 m/s *(1.16 * 60 s) = 286.056 m
d = 418.656 m
Therefore, the average velocity is:
v = d/t =3.23 m/s
