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Semenov [28]
3 years ago
9

One end of a thin rod is attached to a pivot, about which it can rotate without friction. Air resistance is absent. The rod has

a length of 0.35 m and is uniform. It is hanging vertically straight downward. The end of the rod nearest the floor is given a linear speed v0, so that the rod begins to rotate upward about the pivot. What must be the value of v0 such that the rod comes to a momentary halt in a straight-up orientation, exactly opposite to it initial orientation
Physics
1 answer:
Scrat [10]3 years ago
5 0

Answer:

5.24 m/s

Explanation:

So for the rod to be able to rise upward to the straight up position, the kinetic energy caused by linear speed v0 must be just enough to convert into the potential energy.

Since the rod is uniform in mass, we can treat the body as 1 point, at its center of mass, or geometric center, aka 0.35 / 2 = 0.175 m from the pivot.

For the rod to swing from bottom to top, the center must have moved a distance of h = 0.175 * 2 = 0.35 m, vertically speaking.

Since we neglect friction and air resistance, according to the law of energy conservation then:

E_k = E_p

mv^2/2 = mgh

Where v is the speed at the center of mass, g = 9.81 m/s2 is the gravitational acceleration, and m is the mass. We can divide both sides by m

v^2 = 2gh = 2*9.81*0.35 = 6.867

v = \sqrt{6.867} = 2.62 m/s

As this is only the speed at the center of mass, the speed at the bottom end would be different, to calculate this, we need to find the common angular speed:

\omega = v / r = 2.62 / 0.175 = 14.97 rad/s

Where r is the rotation radius, or the distance from pivot point to the center of mass

v_0 = \omega R = 14.97*0.35 = 5.24 m/s

Where R is the distance from the pivot to the bottom end of the rod

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 a substance's density is the same at a certain pressure and temperature, and the density of one substance is usually different than another substance.
4 0
2 years ago
Consider a balloon of mass 0.030kg being inflated with a gas of density 0.54kg/m. What will be the volume of the balloon when it
Nonamiya [84]

the weight of the balloon is .030 * 10 = 0.3 N

the weight of the gas of volume v is 0.54*10 N

The lifting force of a volume of v m³ of displaced air is 1.29v N

so, we need

1.29*10*v = 0.3 + 0.54*10*v

or

1.29v = 0.03+0.54v

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1 year ago
PLEASE PLEASE HELP AND PUT A REAL ANSWER ;-;. ALSO WILL GIVE BRAINLEST!!
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Troposphere

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3 0
3 years ago
A cosmic ray (an electron or nucleus moving ar speeds close to the speed of light) travels across the Milky Way at a speed of 0.
Fiesta28 [93]

Answer:

Cosmic ray's frame of reference: 99,875 years

Stationary frame of reference: 501,891 years

Explanation:

First of all, we convert the distance from parsec into metres:

d=30,000 pc =9.26\cdot 10^{20} m

The speed of the cosmic ray is

v=0.98 c

where

c=3.0 \cdot 10^8 m/s is the speed of light. Substituting,

v=(0.98)(3.0\cdot 10^8)=2.94\cdot 10^8 m/s

And so, the time taken to complete the journey in the cosmic's ray frame of reference (called proper time) is:

T_0 = \frac{d}{v}=\frac{9.26\cdot 10^{20}}{2.94\cdot 10^8}=3.15\cdot 10^{12} s

Converting into years,

T_0 = \frac{3.15\cdot 10^{12}}{(365\cdot 24\cdot 60 \cdot 60}=99,875 years

Instead, the time elapsed in the stationary frame of reference is given by Lorentz transformation:

T=\frac{T_0}{\sqrt{1-(\frac{v}{c^2})^2}}

And substituting v = 0.98c, we find:

T=\frac{99,875}{\sqrt{1-(\frac{0.98c}{c})^2}}=501,891 years

3 0
3 years ago
Over a short interval the coordinate of a car in the meters isgiven by x(t) = 27t - 4.0 t3 where time t is in seconds,at the end
wariber [46]

Answer:

5. -24 m/s²

Explanation:

Acceleration: This can be defined as the rate of change of velocity.

The S.I unit of acceleration is m/s².

mathematically,

a = dv/dt ............................ Equation 1

Where a = acceleration, dv/dt = is the differentiation of velocity with respect to time.

But

v = dx(t)/dt

Where,

x(t) = 27t-4.0t³...................... Equation 2

Therefore, differentiating equation 2 with respect to time.

v = dx(t)/dt = 27-12t²............. Equation 3.

Also differentiating equation 3 with respect to time,

a = dv/dt = -24t

a = -24t .................... Equation 4

from the question,

At the end of 1.0 s,

a = -24(1)

a = -24 m/s².

Thus the acceleration = -24 m/s²

The right option is 5. -24 m/s²

4 0
3 years ago
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