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BARSIC [14]
3 years ago
10

The position vector of a particle of mass 2 kg is given as a function of time by ~r = (5 m) ˆı + (5 m/s)t ˆ . Determine the mag

nitude of the angular momentum of the particle with respect to the origin at time 7 s
Physics
1 answer:
Slav-nsk [51]3 years ago
7 0

Answer:

L = 50 \hat{k}\ kg.m^2/s

Explanation:

given,

mass of the particle = 2 Kg

position vector of the particle is given as

r = 5\hat{i} + 5 t \hat{j}

v =\dfrac{dr}{dt}

\dfrac{dr}{dt} = 5 \hat{j}

angular momentum

L = m (r x v)

L = m[(5\hat{i} + 5 t \hat{j}\ )\times (5 \hat{j})]

cross product of vectors

i x j = k

j x j = 0

L = m\times 25 \hat{k}

L = 2\times 25 \hat{k}

L = 50 \hat{k}\ kg.m^2/s

Angular momentum is not dependent on the time function.

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demonstrate in a brief paragraph how the search to explain planetary orbits exemplifies the scientific method and then use of mo
kari74 [83]

Answer:

People firstly believe that the planets move in a circular orbit until Newton came up with his hypothesis by inventing calculus so that we could understood and calculated planetary orbits and their accuracy.

Explanation:

  • Everyone assumed the planets were perfect circles until Newton came up with an idea. Slowly people would make maps of the orbits that added circles on circles, and they could never really explain about the movement of the planet. They simply say that planets move on circles but they lacked the math to explain or prove it. Then Newton came up with an idea of inventing calculus so that we could understood and calculated planetary orbits and their accuracy.
  • Firstly people used their observations and say that the orbits looked like circles, then they developed their models and did the math, and proposed their hypothesizes which were wrong, until Newton came along and tried to match a model that used elliptical orbits and invented the math that allowed him to make predictions with it. His model worked for most planets.
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8 0
3 years ago
What average force is needed to accelerate a 7.00-gram pellet from rest to 155 m/s over a distance of 0.600 m along the barrel o
leonid [27]

Answer: The force needed is 140.22 Newtons.

Explanation:

The key assumption in this problem is that the acceleration is constant along the path of the barrel bringing the pellet from velocity 0 to 155 m/s. This means the velocity is linearly increasing in time.

The force exerted on the pellet is

F = m a

In order to calculate the acceleration, given the displacement d,  

d = \frac{1}{2}at^2\implies a=\frac{2d}{t^2}

we will need to determine the time t it took for the pellet to make the distance through the barrel of 0.6m. That time can be determined using the average velocity of the pellet while traveling through the barrel. Since the velocity is a linear function of time, as mentioned above, the average is easy to calculate as:

\overline{v}=\frac{1}{2}(v_{end}-v_{start})=\frac{1}{2}(155-0)\frac{m}{s}=77.5\frac{m}{s}

This value can be used to determine the time for the pellet through the barrel:

t = \frac{d}{\overline{v}}=\frac{0.6m}{77.5\frac{m}{s}}\approx0.00774s

Finally, we can use the above to calculate the force:

F = ma = m\frac{2d}{t^2} = 0.007kg\cdot \frac{2\cdot 0.6 m}{0.00774^2 s^2}\approx 140.22N



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