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3 years ago

What is the timeline for the law of conservation of energy

1 answer:

4 0

In 1842, Julius Robert Mayer discovered The law of conservation of Energy. It its most compact form, it it now called The first law of Thermodynamics

Energy can neither be created nor destroyed, it can only be changed to another form of energy.

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

victus00 [196]

Answer:

a)- 1.799 rad/sec²

b)- 17.6 x 10ˉ³Nm

Explanation:

ω₀ = 720 rev/min x (1 min/60 sec) x (2π rad / 1 rev) = 24π rad/s

a) Assuming a constant angular acceleration, the formula will be

α = (ωf -ω₀) / t

As final state of the grindstone is at rest, so ωf =0

⇒ α = (0-24π) / 41.9 = - 1.799 rad/sec²

b)Moment of inertia I for a disk about its central axis

I = ½mr²

where m=2kg and radius 'r'= 0.099m

I = ½(2)(0.099²)

I = 9.8 x 10ˉ³ kgm²

Next is to determine the frictional torque exerted on the grindstone, that caused it to stop, applying the rotational equivalent of the Newton's 2nd law:

τ = I α =>(9.8 x 10ˉ³)(- 1.799)

τ = - 17.6 x 10ˉ³Nm

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

8 0

3 years ago

Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 AM, each heading for Wildwood. One car’s average speed is 10

olganol [36]

Answer:

The average speed of the cars is 50mph

Explanation:

Option C

4 0

3 years ago

The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were obser

ELEN [110]

Answer:

a) v² = G M R³, b) T = 2π / $\sqrt{GMR}$ , c) $m \sqrt{GMR^5 }$

Explanation:

a) The kinetic energy is

K = ½ m v²

to find the velocity let's use Newton's second law

F = m a

acceleration is centripetal

a = v² / R

force is the universal force of attraction

F = G m M / r²

we substitute

G m M R² = m v² R

v² = G M R³

the kinetic energy is

K = ½ m G M R³

b) angular and linear velocity are related

v = w R

w = v / R

w = $\frac{\sqrt{GMR^3 }}{R}$

w = $\sqrt{GMR}$

the angular velocity is related to the period

w = 2π / T

T = 2π / w

we substitute

T = 2π / $\sqrt{GMR}$

c) the angular moeomto is

L = m v r

L = m RA G M R³ R

L = $m \sqrt{GMR^5 }$

4 0

3 years ago

A screw can be considered a type of

Pavel [41]

Fastener because a fastener is something that connects to objects and usually can come apart but can also be permanent

8 0

3 years ago

A)Calculate the effective value of g, the acceleration of gravity, at 7900 m above the Earth's surface.

arsen [322]

The solution for the acceleration of gravity is given as

$g_{1}=9.789 \mathrm{~m} / \mathrm{s}^{2}$$

$g_2=1.955 \mathrm{~m} / \mathrm{s}^{2}$$

This is further explained below.

<h3>What is the effective value of g, the acceleration of gravity, at 7900 km above the Earth's surface.?</h3>

Generally,

Mass of earth $M=5.97 \times 10^{24} \mathrm{~kg}$

Radius of earth $R=6371 \mathrm{~km}$

Gravitational const. $G=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2}$

height $h_{1}=7900 \mathrm{~m}=7.9 \mathrm{~km}$$$

$R+h_{1}=6371+7.9 &\\\\R+h_{1}=6378.9 \mathrm{~km} \\\\&R+h_{1}=6378.9 \times 10^{3} \mathrm{~m}\end{aligned}$

In conclusion, acceleration due to gravity at this point will be

$g_{1}=\frac{G M}{\left(\bar{R}+\overline{h_{1}}\right)^{2}}$\\\\$g_{1}=\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{\left(6378.9 \times 10^{3}\right)^{2}}$\\\\$g_{1}=9.789 \mathrm{~m} / \mathrm{s}^{2}$$

for $h_{2}=7900 \mathrm{~km}$

$R+h_{2}=6371+7900\\\\R+h_{2}=14271 \mathrm{~km}\\\\$g_{2}=\frac{6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{\left(14271 \times 10^{3}\right)^{2}}$\\\\$g_2=1.955 \mathrm{~m} / \mathrm{s}^{2}$$

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5 0

2 years ago