When a closed loop of wire experiences a changing magnetic field a voltage and therefore current is produced. This is the basis
2 answers:
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Answer:
w = 0.943 rad / s
Explanation:
For this problem we can use the law of conservation of angular momentum
Starting point. With the mouse in the center
L₀ = I w₀
Where The moment of inertia (I) of a rod that rotates at one end is
I = 1/3 M L²
Final point. When the mouse is at the end of the rod
= I w + m L² w
As the system is formed by the rod and the mouse, the forces during the movement are internal, therefore the angular momentum is conserved
L₀ = L_{f}
I w₀ = (I + m L²) w
w = I / I + m L²) w₀
We substitute the moment of inertia
w = 1/3 M L² / (1/3 M + m) L² w₀
w = 1 / 3M / (M / 3 + m) w₀
We substitute the values
w = 1/3 / (1/3 + 0.02) w₀
w = 0.943 w₀
To finish the calculation the initial angular velocity value is needed, if we assume that this value is w₀ = 1 rad / s
w = 0.943 rad / s
(a) 0.8 m/s^2
The force exerted on the sled is F = 4.0 N. We can calculate the acceleration of the sled by using Newton's second law:
where
m = 5.0 kg is the mass of the sled
a is the acceleration of the sled
Solving the equation for a, we find:
(b) 0.098 m/s^2
According to Newton's third law (action-reaction law), since the girl exerts a force on the sled, then the sled exerts an equal and opposite force on the girl as well. This means that the force exerted on the girl is also F = 4.0 N. As before, we can calculate the acceleration of the girl by using Newton's second law:
where
m = 41 kg is the mass of the girl
a is the acceleration of the girl
Solving the equation for a, we find:
(c) 5.8 s
Taking the initial position of the girl as x = 0, the position at time t of the girl is given by:
where is the acceleration of the girl.
The sled starts instead its motion from x = 15 m, so its position at time t is given by
where is the acceleration of the sled, and the negative sign is due to the fact that the sled accelerates in opposite direction to the girl's acceleration.
The girl and the sled meet when x(t) = x'(t). So, we find: