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shutvik [7]
3 years ago
8

If two objects A and B have the same kinetic energy but A has three times the momentum of B, what is the ratio of their inertias

?
Physics
1 answer:
Thepotemich [5.8K]3 years ago
7 0

Answer:

\frac{inertia_B}{inertia_A}=9

Explanation:

First of all, let's remind that:

- The kinetic energy of an object is given by K=\frac{1}{2}mv^2, where m is the mass and v is the speed

- The momentum of an object is given by p=mv

- The inertia of an object is proportional to its mass, so we can write I=km, where k just indicates a constant of proportionality

In this problem, we have:

- K_A = K_B (the two objects have same kinetic energy)

- p_A = 3 p_B (A has three times the momentum of B)

Re-writing both equation we have:

\frac{1}{2}m_A v_A^2 = \frac{1}{2}m_B v_B^2\\m_A v_A = 3 m_B v_B

If we divide first equation by second one we get

v_A = 3 v_B

And if we substitute it into the first equation we get

m_A (3 v_B)^2 = m_B v_B^2\\9 m_A v_B^2 = m_B v_B^2\\m_B = 9 m_A

So, B has 9 times more mass than A, and so B has 9 times more inertia than A, and their ratio is:

\frac{I_B}{I_A}=\frac{km_B}{km_A}=\frac{9m_A}{m_A}=9

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A jet liner must reach a speed of 82 m/s for takeoff. If the
SIZIF [17.4K]

Answer:

The acceleration that the jet liner that must have is 2.241 meters per square second.

Explanation:

Let suppose that the jet liner accelerates uniformly. From statement we know the initial (v_{o}) and final speeds (v_{f}), measured in meters per second, of the aircraft and likewise the runway length (d), measured in meters. The following kinematic equation is used to calculate the minimum acceleration needed (a), measured in meters per square second:

a = \frac{v_{f}^{2}-v_{o}^{2}}{2\cdot d}

If we know that v_{o} = 0\,\frac{m}{s}, v_{f} = 82\,\frac{m}{s} and d = 1500\,m, then the acceleration that the jet must have is:

a = \frac{\left(82\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}}{2\cdot (1500\,m)}

a = 2.241\,\frac{m}{s^{2}}

The acceleration that the jet liner that must have is 2.241 meters per square second.

3 0
2 years ago
A lab cart with a mass of 15 kg is moving with constant velocity, v, along a straight horizontal track. A student drops a 2 kg m
lbvjy [14]

The equation 15v_{i} + 2*0 = (15 + 2)v_{f} (option 3) represents the horizontal momentum of a 15 kg lab cart moving with a constant velocity, v, and that continues moving after a 2 kg object is dropped into it.  

The horizontal momentum is given by:

p_{i} = p_{f}

m_{1}v_{1}_{i} + m_{2}v_{2}_{i} = m_{1}v_{1}_{f} + m_{2}v_{2}_{f}

Where:

  • m₁: is the mass of the lab cart = 15 kg
  • m₂: is the <em>mass </em>of the object dropped = 2 kg
  • v_{1}_{i}: is the initial velocity of the<em> lab cart </em>
  • v_{2}_{i}: is the <em>initial velocit</em>y of the <em>object </em>= 0 (it is dropped)
  • v_{1}_{f}: is the final velocity of the<em> lab cart </em>
  • v_{2}_{f}: is the <em>final velocity</em> of the <em>object </em>

Then, the horizontal momentum is:

15v_{1}_{i} + 2*0 = 15v_{1}_{f} + 2v_{2}_{f}

When the object is dropped into the lab cart, the final velocity of the lab cart and the object <u>will be the same</u>, so:

15v_{1}_{i} + 2*0 = v_{f}(15 + 2)

Therefore, the equation 15v_{i} + 2*0 = (15 + 2)v_{f} represents the horizontal momentum (option 3).

Learn more about linear momentum here:

  • brainly.com/question/2141713?referrer=searchResults
  • brainly.com/question/2400186?referrer=searchResults

I hope it helps you!            

4 0
2 years ago
Why are renewable energy resources going to be important in our future
marshall27 [118]
Renewable resources are going to be important in our future because if we use up all of our NON-renewable resources now, then we’ll still have the renewable resources to depend on.
I hope this helped! :-)
3 0
3 years ago
Ahsoka pulls a wounded soldier (mass 64 kg) across the ground with a force 18 Newtons. If they have an acceleration of 1.5 m/s2
Kryger [21]

Answer:

0.124

Explanation:

18-(9.81*64)*k=64*1.5

4 0
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