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vazorg [7]
3 years ago
14

There is a plate with moment of inertia Ip = 0.0711 kgm2 , rotating around its center of mass with angular speed of 4.53 rad/s.

You carefully put a ring with moment of inertia Ir = 0.0353 kgm2 , on the plate, center to center of plate and they rotate with same angular speed later. Ignore all the friction other than the one between the plate and the ring. Please (a) calculate their common angular speed; (b) the kinetic energy loss during this process.
Physics
1 answer:
Anna007 [38]3 years ago
5 0

Answer:

1) their common angular speed = 3.038 rad/s

2) kinetic energy loss = 0.24J

Explanation:

1) This is a case of conservation of angular momentum.

The initial angular momentum must be equal to the final angular momentum

Initial angular momentum = I x w

Where I = moment of inertia, and

w = angular momentum.

Initial angular momentum = 0.0711 x 4.53 = 0.322 kg-m2-rad/s

After addition of ring, moment of inertia becomes,

0.0711 + 0.0353 = 0.106 kg-m2

Therefore, final angular momentum will be

0.106 x Wf

Where Wf = final common angular velocity

Equating the two angular momentum we have

0.322 = 0.106Wf

Wf = 0.322/0.106 = 3.038 rad/s

2) KE = 1/2 x I x w^2

Initial KE = 1/2 x 0.0711 x 4.53^2

= 0.729 J

Final KE = 1/2 x 0.106 x 3.038^2

= 0.489 J

Loss in KE = 0.729 - 0.489 = 0.24 J

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Triss [41]

The acceleration of the boat is 2 m/s^2 (eastward)

Explanation:

We can solve this problem by using Newton's second law, which states that:

F = ma (1)

where

F is the net force on a body

m is its mass

a is its acceleration

First of all, we have to find the net force acting on the boat. We have:

- The force of the motor, 100 N eastward

- The force of the air resistance, 60 N westward

So the net force is:

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Now we can apply eq.(1), using:

F = 40 N

m = 20 kg (mass of the boat)

and solving for a, we find the acceleration:

a=\frac{F}{m}=\frac{40}{20}=2.0 m/s^2

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ra1l [238]

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Explanation:

8 0
3 years ago
An 800 kHz radio signal is detected at a point 3.2 km distant from a transmitter tower. The electric field amplitude of the sign
hammer [34]

Answer:

1.07 nT

Explanation:

We know that E/B = c where E = electric field amplitude = 320 mV/m = 0.32 V/m, B = magnetic field amplitude and c = speed of light = 3 × 10⁸ m/s.

So, B = E/c

Substituting E and c into B, we have

B = E/c

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3 0
3 years ago
Falling objects drop with an average acceleration of 9.8 m/s2. An arrow is shot with a velocity of 11.76 m/s straight down from
In-s [12.5K]

Answer:

3.8 secs

Explanation:

Parameters given:

Acceleration due to gravity, g = 9.8 m/s^2

Initial velocity, u = 11.76 m/s

Final velocity, v = 49 m/s

Using one of Newton's equations of linear motion, we have that:

v = u + gt

where t = time of flight of arrow

The sign is positive because the arrow is moving downward, in the same direction as gravitational force.

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6 0
3 years ago
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