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katrin [286]
3 years ago
7

The Moon and Earth rotate about their common center of mass, which is located about RcM 4700 km from the center of Earth. (This

is 1690 km below the surface.) Take the distance from the center of the earth to the center of the moon to be 3.84x108 m, and the mass of the moon to be 7.35x1022 kg Part (a) Write an expression for the acceleration of Earth due to the Moon's gravity using M as the mass of the moon and R as the distance between the center of the Earth and the center of the Moon. Expression: ам- Select from the variables below to write your expression. Note that all variables may not be required. a, B, T, 0, d, g. G, h, j, k, M, P, R, RCM t Part (b) Calculate the acceleration of Earth due to the Moon's gravity in ms Numeric :A numeric value is expected and not an expression. ам Part (c) Calculate the centripetal acceleration of the center of Earth as it rotates about their common center of mass once each lunar month (about 27.3 d) in m/s2 Numeric :A numeric value is expected and not an expression.
Physics
1 answer:
erica [24]3 years ago
3 0

To solve this problem it is necessary to apply the concepts related to gravity as an expression of a celestial body, as well as the use of concepts such as centripetal acceleration, angular velocity and period.

PART A) The expression to find the acceleration of the earth due to the gravity of another celestial body as the Moon is given by the equation

g = \frac{GM}{(d-R_{CM})^2}

Where,

G = Gravitational Universal Constant

d = Distance

M = Mass

R_{CM} = Radius earth center of mass

PART B) Using the same expression previously defined we can find the acceleration of the moon on the earth like this,

g = \frac{GM}{(d-R_{CM})^2}

g = \frac{(6.67*10^{-11})(7.35*10^{22})}{(3.84*10^8-4700*10^3)^2}

g = 3.4*10^{-5}m/s^2

PART C) Centripetal acceleration can be found throughout the period and angular velocity, that is

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

At the same time we have that centripetal acceleration is given as

a_c = \omega^2 r

Replacing

a_c = (\frac{2\pi}{T})^2 r

a_c = (\frac{2\pi}{26.3d(\frac{86400s}{1days})})^2 (4700*10^3m)

a_c = 3.34*10^{-5}m/s^2

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Marianna [84]
The value of 'g' is not affected by rotation at any place on Earth.
7 0
3 years ago
Recall that the spring constant is inversely proportional to the number of coils in the spring, or that shorter springs equate t
ruslelena [56]

Answer:

x_1= 0.0425m

Explanation:

Using the tension in the spring and the force of the tension can by describe by

T = kx

, T = mg

Therefore:

m*g = k*x

With two springs, let, T1 be the tension in each spring,  x1 be the extension of each spring.  The spring constant of each spring is 2k so:

T_1 = 2k*x_1

2T_1 = m*g=4k x_1

Solve to x1

x_1=\frac{m*g}{4k}

x_1=\frac{k*x}{4*k}

x_1=\frac{x}{4}

x_1 = 0.170 / 4

x_1= 0.0425m

7 0
3 years ago
A ball has a mass of 1.5kg and is thrown straight up with a speed of 60m/s, what is the ball’s momentum:
madam [21]

Answer:

Assumption: the air resistance on this ball is negligible. Take g = 10\; \rm m \cdot s^{-2}.

a. The momentum of the ball would be approximately 60\;\rm kg \cdot m \cdot s^{-1} two seconds after it is tossed into the air.

b. The momentum of the ball would be approximately \rm \left(-45\; \rm kg \cdot m \cdot s^{-1}\right) three seconds after it reaches the highest point (assuming that it didn't hit the ground.) This momentum is smaller than zero because it points downwards.

Explanation:

The momentum p of an object is equal its mass m times its velocity v. That is: \vec{p} = m \cdot \vec{v}.

Assume that the air resistance on this ball is negligible. If that's the case, then the ball would accelerate downwards towards the ground at a constant g \approx -10\; \rm m \cdot s^{-2}. In other words, its velocity would become approximately 10\; \rm m \cdot s^{-1} more negative every second.

The initial velocity of the ball is 60\; \rm m \cdot s^{-1}. After two seconds, its velocity would have become 60\;\rm m \cdot s^{-1} + 2\; \rm s \times \left(-10\;\rm m \cdot s^{-1}\right) = 40\; \rm m \cdot s^{-1}. The momentum of the ball at that time would be around p = m \cdot v \approx 60\; \rm kg \cdot m \cdot s^{-1}.

When the ball is at the highest point of its trajectory, the velocity of the ball would be zero. However, the ball would continue to accelerate downwards towards the ground at a constant g \approx -10\; \rm m \cdot s^{-2}. That's how the ball's velocity becomes negative.

After three more seconds, the velocity of the ball would be 0\; \rm m \cdot s^{-1} + 3\; \rm s \times \left(-10\; \rm m \cdot s^{-2}\right) = -30 \; \rm m \cdot s^{-1}. Accordingly, the ball's momentum at that moment would be p = m \cdot v \approx \left(-45\; \rm kg \cdot m \cdot s^{-1}\right).

3 0
3 years ago
Someone please help me
Lapatulllka [165]
False... I hope that helps ;)
6 0
3 years ago
A mass hanging from a spring oscillates with a period of 0.35 s. Suppose the mass and spring are swung in a horizontal circle, w
Annette [7]

Answer:

66 rpm

Explanation:

The period of oscillation is given by

T=2\pi \sqrt{\frac {m}{k}}

\frac {k}{m}=\frac {4\pi^{2}}{T^{2}} where  T is time period of oscillation which is given as 0.35 s, k s spring constant and m is the mass of the object attached to the spring.

Also, net force is given by

Net force=m\omega^{2} L

\omega=\sqrt{\frac {k\triangle L}{mL}} where \triangle L is the elongation, L is original length, \omega is the angular velocity

Substituting the equation of \frac {k}{m} into the above we obtain

\omega=\sqrt {\frac {4\pi^{2}\triangle L}{T^{2} L}}

\omega=\sqrt {4\pi^{2}\times 0.15L}{0.35^{2}\times L}}=6.952763\approx 6.95 rad/s

6.95\times\frac {60 s}{2\pi rad}\approx 66 rpm

6 0
3 years ago
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