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Setler [38]
3 years ago
15

A torsional pendulum is formed by attaching a wire to the center of a meter stick with a mass of 5.00 kg. If the resulting perio

d is 4.00 min, what is the torsion constant for the wire
Physics
1 answer:
White raven [17]3 years ago
5 0

Answer:

The torsion constant for the wire is 2.856\times 10^{-4}\,N\cdot m.

Explanation:

The angular frequency of the torsional pendulum (\omega), measured in radians per second, is defined by the following expression:

\omega = \sqrt{\frac{\kappa}{I} } (1)

Where:

\kappa - Torsional constant, measured in newton-meters.

I - Moment of inertia, measured in kilogram-square meters.

The angular frequency and the moment of inertia are represented by the following formulas:

\omega = \frac{2\pi}{T} (2)

I = \frac{m\cdot L^{2}}{12} (3)

Where:

T - Period, measured in seconds.

m - Mass of the stick, measured in kilograms.

L - Length of the stick, measured in meters.

By (2) and (3), (1) is now expanded:

\frac{2\pi}{T} = \sqrt{\frac{12\cdot \kappa}{m\cdot L^{2}} }

\frac{2\pi}{T} = \frac{2}{L}\cdot \sqrt{\frac{3\cdot \kappa}{m} }

\frac{\pi\cdot L}{T} = \sqrt{\frac{3\cdot \kappa}{m} }

\frac{\pi^{2}\cdot L^{2}}{T^{2}} = \frac{3\cdot \kappa}{m}

\kappa = \frac{\pi^{2}\cdot m\cdot L^{2}}{3\cdot T^{2}}

If we know that m = 5\,kg, L = 1\,m and T = 240\,s, then the torsion constant for the wire is:

\kappa = \frac{\pi^{2}\cdot (5\,kg)\cdot (1\,m)^{2}}{3\cdot (240\,s)^{2}}

\kappa = 2.856\times 10^{-4}\,N\cdot m

The torsion constant for the wire is 2.856\times 10^{-4}\,N\cdot m.

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sashaice [31]
1) The minute travels the circumference of a 4 inches circle is 60 minutes:

Circumference = 2πr = 2π(2in) = 4π in
Time = 60 minutes

2) Constant angular velocity => (4π / 60) = (x / 20) => x = 4π / 3 inches

x = 4.19 inches

Answer: 4.19 inches

4 0
3 years ago
a street light is mounted at the top of a 15 foot pole. A man 6 ft tall walks away from the pole wit a speed of 7 ft/s along a s
Mariulka [41]

Answer:

16.3 ft/s

Explanation:

Let d=distance

and

x = length of shadow.

Therfore,

x=(d + x)

 = 6/15

So,

    15x = 6x + 6d

     9x = 6d.

x = (2/3)d.

As we know that:

dx=dt

   = (2/3) (d/dt) 

Also,

Given:

d(d)=dt

     = 7 ft/s

Thus,

d(d + x)=dt

           = (7/3)d (d/dt)

Substitute, d= 7  

d(d + x) = 49/3 ft/s.

Hence,

d(d + x) = 16.3 ft/s.

4 0
3 years ago
You throw a basketball and a tennis ball across the classroom so that each ball has the exact same momentum. Explain how this is
Helga [31]

Answer:

It is possible by increasing the speed of the tennis ball by a factor of (Mass of the tennis ball)/(Mass of the basketball)

Explanation:

The momentum of a body = The bod's mass × The body's velocity

Therefore, the momentum of a given mass of an object, such as a tennis ball can be increased by increasing the velocity or speed of the object. Whereby the speed of the ball, v₁, is increased such that the momentum of the basketball and the tennis ball will be the same, is given by the following equation

Mass of the basketball × v₂ = Mass of the tennis ball × v₁

Therefore, v₁/v₂ = (Mass of the tennis ball)/(Mass of the basketball)

7 0
3 years ago
sara and tory are out fishing on the lake on a hot summer day when they both decide to go for a swim. sara dives off the front o
crimeas [40]

Here it is an application of Newton's III law

as we know by Newton's III law that every action has equal and opposite reaction

So here as we know that two boys jumps off the boat with different forces

from front side of the boat the boy jumps off with force 45 N which means as per Newton's III law if boy has a force of 45 N in forward direction then he must apply a reaction force on the boat in reverse direction of same magnitude

So boat must have an opposite force on front end with magnitude 45 N

Now similar way we can say

from back side of the boat the boy jumps off with force 60 N which means as per Newton's III law if boy has a force of 60 N in backward direction then he must apply a reaction force on the boat in reverse direction of same magnitude

So boat must have an opposite force on front end with magnitude 60 N

So here net force due to both jump on the boat is given by

F_{net} = F_1 - F_2

F_{net} = 60 - 45

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3 0
3 years ago
Which has the most momentum?
boyakko [2]

Answer:

Both objects have the same magnitude of momentum.

Explanation:

If an object of mass m is moving at a velocity of v, the momentum of that object would be m\, v.

The 100\; {\rm g} (0.1\; {\rm kg}) object is moving at a speed of 1\; {\rm m\cdot s^{-1}}. The magnitude of the momentum of this object would be 0.1\; {\rm kg} \times 1\; {\rm m\cdot s^{-1}} = 0.1\; {\rm kg \cdot m \cdot s^{-1}}.

Similarly, the momentum of the 1\; {\rm g} (10^{-3}\; {\rm kg}) object moving at a speed of 100\; {\rm m\cdot s^{-1}} would be 10^{-3}\; {\rm kg} \times 100\; {\rm m\cdot s^{-1}} = 0.1\; {\rm kg \cdot m \cdot s^{-1}}.

Hence, the magnitude of momentum is the same for the two objects.

7 0
2 years ago
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