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il63 [147K]
3 years ago
7

A firm wants to determine the amount of frictional torque in their current line of grindstones, so they can redesign them to be

more energy efficient. To do this, they ask you to test the best-selling model, which is basically a diskshaped grindstone of mass 1.5 kg and radius 7.40 cm which operates at 730 rev/min. When the power is shut off, you time the grindstone and find it takes 38.8 s for it to stop rotating.
(a) What is the angular acceleration of the grindstone in rad/s^2? (Assume constant angular acceleration.)


(b) What is the frictional torque exerted on the grindstone in N·m?
Physics
1 answer:
OLEGan [10]3 years ago
3 0

Answer:

a) -1.97 rad/sec² b) -8.09*10⁻³ N.m

Explanation:

a) Assuming a constant angular acceleration, we can apply the definition of angular acceleration, as follows:

γ = (ωf -ω₀) / t

We know that the final state of the grindstone is at rest, so ωf =0

In order to be consistent in terms of units, we can convert ω₀ from rev/min to rad/sec:

ω₀ = 730 rev/min* (1 min/60 sec)* (2*π rad / 1 rev) = 73/3*π

⇒ γ = (0-73/3*π) / 38.8 sec = - 1.97 rad/sec²

b) In order to get the value of the frictional torque exerted on the grindstone, that caused it to stop, we can apply the rotational equivalent of the Newton's 2nd law, as follows:

τ = I * γ (1)

As the grindstone can be approximated by a solid disk, the rotational inertia I can be expressed as follows:

I = m*r² / 2, where m=1.5 kg and r = 0.074 m.

Replacing in (1) , m. r and γ (the one we calculated in a)), we get:

τ = (1.5 kg* (0.074)² m² / 2) * -1.97 rad/sec = -8.09*10⁻³ N.m

(The negative sign implies that the frictional torque opposes to the rotation of the grindstone).

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igomit [66]

Answer:

t'=1.1897*10^{-6} s

t'=1.1897 μs

Explanation:

First we will calculate the velocity of micrometeorite relative to spaceship.

Formula:

u=\frac{u'+v}{1+\frac{u'*v}{c^{2}}}

where:

v is the velocity of spaceship relative to certain frame of reference =  -0.82c (Negative sign is due to antiparallel track).

u is the velocity of micrometeorite relative to same frame of reference as spaceship = .82c (Negative sign is due to antiparallel track)

u' is the relative velocity of micrometeorite with respect to spaceship.

In order to find u' , we can rewrite the above expression as:

u'=\frac{v-u}{\frac{u*v}{c^{2} }-1 }

u'=\frac{-0.82c-0.82c}{\frac{0.82c*(-0.82c)}{c^{2} }-1 }

u'=0.9806c

Time for micrometeorite to pass spaceship can be calculated as:

t'=\frac{length}{Relatie seed (u')}

t'=\frac{350}{0.9806c}     (c = 3*10^8 m/s)

t'=\frac{350}{0.9806* 3.0*10^{8} }

t'=1.1897*10^{-6} s

t'=1.1897 μs

4 0
3 years ago
Una ola oceánica viaja a aproximadamente 1,97 m / s. Esto es 4 millas por hora. La frecuencia de las ondas es de aproximadamente
yKpoI14uk [10]

Answer:

λ = 28,14 m

Explanation:

To find the wavelength of the wave you use the following formula:

v=\lambda f  (1)

v: speed of the wave = 1,97 m/s

λ: wavelength

f: frequency of the wave = 0,07 Hz

You replace the values of v and f in the equation (1) and solve for λ:

\lambda=\frac{v}{f}=\frac{1,97m/s}{0,07Hz}=28,14m

hence, the wavelength of the wave is 28,14 m

5 0
3 years ago
Your shopping cart has a mass of 65 kilograms, In order to accelerate the shopping cart down an aisle at 0.3 m/sec2, what force
garri49 [273]
Remember Newton's second law: F=ma

to get the force in newtons, mass should be in kg and acceleration in m/s^2

conveniently, we don't need to convert units

we just need to multiply the two to get the force

65* 0.3 = 19.5 kg m/s^2 or N

if significant digit is an issue, the least number if sig figs is 1 so the answer would be 20 N
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A ball hits a wall horizontally at 6m/s and rebounces at 4.4m/s the ball is in contact with wall for 0.04 sec. what is the accel
Svetlanka [38]

Answer:

Acceleration (a) = 40 m/s²

Explanation:

Given:

Initial velocity (u) = 6 m/s

Final velocity (v) = 4.4 m/s

Time taken (t) = 0.04sec

Find:

Acceleration (a) = ?

Computation:

We know that,

⇒ v = u + at

⇒ a = (v - u) / t

⇒ Acceleration (a) = (4.4 - 6) / 0.04

⇒ Acceleration (a) = (-1.6) / 0.04

Acceleration (a) = 40 m/s²

8 0
3 years ago
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