Answer:
217.04 rad/s
Explanation:
We are given that
Initial velocity,
t=10 s
Number of rev=20
We have to find the angular velocity at t=24 s








Substitute the values


Substitute the value of k and t=24

The magnitude of force acting on wire will be 1.90 N and the direction of the force acting on the wire will be 41.9 degrees below the negative y axis.
Explanation:
It is known that the force acting on a current carrying conductor placed in a magnetic field is

Here B is the magnetic field, I is the current flowing through the wire and L is the length of the wire which is given as 44 cm.
Since the wire is bended in the middle at right angle so the length of the two sides of the wire will be 22 cm each. Also one part is lying over z axis and another part lies in the plane of xy in the equation of line y = 2x. So the slope of this wire will be

This will be equal to tan θ.
So θ = tan⁻¹ (2) =63.4°
Then, the length of the wire will be written as components of i, j and k.


Then,
F = I (L × B)

![F = 20.5 (\left[\begin{array}{ccc}i&j&k\\0.098&0.197&-0.22\\0.316&0&0\end{array}\right] )](https://tex.z-dn.net/?f=F%20%3D%2020.5%20%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0.098%260.197%26-0.22%5C%5C0.316%260%260%5Cend%7Barray%7D%5Cright%5D%20%29)


The magnitude of force on the wire will be

And the direction can be found by the tan inverse of the ratio of k component to j component of the force.

So the magnitude of force acting on wire will be 1.90 N and the direction of the force acting on the wire will be 41.9 degrees below the negative y axis.
Answer:
Total heat transfer is positive
Total work transfer is positive
Explanation:
The first law of thermodynamics states that when a system interacts with its surrounding, the amount of energy gained by the system must be equal to the amount of energy lost by the surrounding. In a closed system, exchange of energy with the surrounding can be done through heat and work transfer.
Heat transfer to a system is positive and that transferred from the system is negative.
Also, work done by a system is positive while the work done on the system is negative.
Therefore, from the question, since the heat engine inputs 10kJ of heat, then heat is being transferred to the system. Hence, the sign of the total heat transfer is positive (+ve)
Also, since the heat engine outputs 5kJ of work, it implies that work is being done by the system. Hence the sign of the total work transfer is also positive (+ve).