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Murrr4er [49]
3 years ago
14

A 13kg box slides 4.0m down the frictionless ramp shown in the figure , then collides with a spring whose spring constant is 170

N/m.
What is the maximum compression of the spring?
At what compression of the spring does the box have its maximum speed?

Physics
1 answer:
Svetradugi [14.3K]3 years ago
7 0
The force on the box is:
F = mgsin∅
If we multiply by this with the distance it traveled, we will know the work done by the box. 
W = dmgsin∅

This work will be converted to elastic potential energy in the spring which is:
1/2 kx². Equating these and substituting values:
1/2 * 170 * x² = 4 * 13 * 9.81 * sin(30)
x = 1.73 m

The box's maximum speed will at the point right before contact with the spring, when the compression is 0.
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Answer:

a) Team A will win.

b) The losing team will accelerate towards the middle line with 0.01 m/s^{2}

Explanation:

Given that Team-A pulls with a force , F_{1} = 50N

and Team-B pulls with a force , F_{1} = 45N

∵ F_{1} > F_{2}

The rope will move in the direction of force F_{1}.

∴ Team-A will win.

b) Considering both the teams as one system of total mass , m = 246+253 = 499 kg

Net force on the system , F = F_{1} - F_{2} = 50-45 = 5N

Applying Newtons first law to the system ,

F = ma , where 'a' is the acceleration of the system.

Since , both the teams are connected by the same rope , their acceleration would be the same.

∴ 5 = 499×a

∴ a = 0.01 m/s^{2}

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Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular alumin
Zarrin [17]

Answer:

\rm 9.186\times 10^{-7}\ C.

Explanation:

<u>Given:</u>

  • Diameter of the plates of the capacitor, D = 21 cm = 0.21 m.
  • Distance of separation between the plates, d = 1.0 cm = 0.01 m.
  • Minimum value of electric field that produces spark, \rm E=3\times 10^6\ N/C.

When the dimensions of the plate of the capacitor is comparatively much larger than the distance of separation between the plates, then, according to the Gauss' law of electrostatics, the value of the electric field strength in the region between the plates of the capacitor is given by

\rm E=\dfrac{\sigma}{\epsilon_o}.

where,

  • \rm \sigma = surface charge density of the plate of the capacitor = \dfrac qA.
  • \rm q = magnitude of the charge on each of the plate.
  • \rm A = surface area of each of the plate =\rm \pi \times (Radius)^2=\pi \times\left ( \dfrac{D}{2}\right )^2= \pi \times \left ( \dfrac{0.21}{2}\right )^2=3.46\times 10^{-2}\ m^2.
  • \epsilon_o = electrical permittivity of free space, having value = 8.85\times 10^{-12}\rm \ C^2N^{-1}m^{-2}.

For the minimum value of electric field that produces spark,

\rm E = \dfrac{q}{A\epsilon_o}\\\Rightarrow q = E\ A\epsilon_o\\=3\times 10^6\times 3.46\times 10^{-2}\times 8.85\times 10^{-12}\\=9.186\times 10^{-7}\ C.

It is the maximum value of the magnitude of charge which can be added up to each of the plates of the capacitor.

4 0
3 years ago
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