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Deffense [45]
3 years ago
8

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circ

ular, determine the mass of Mars. (kg)
Physics
1 answer:
FromTheMoon [43]3 years ago
6 0

Answer:

6.27*10^{23}kg

Explanation:

assume

M= mass of Mars

m=mass of phobos

r=orbital radius

T=period

we can apply F=ma to this orbital motion (considering the cricular motion laws)

where,

F=\frac{GMm}{r^{2} }  and a=rω^2

where ω=\frac{2\pi }{T} and G is the universal gravitational constant.

G = 6.67 x 10-11 N m2 / kg2

F=ma\\\frac{GMm}{r^{2} }=mr(\frac{2\pi }{T} )^{2}\\  M=\frac{r^{3}}{G}  (\frac{2\pi }{T} )^{2}\\M=\frac{(9.4*10x^{6} )^{3}*(2\pi )^{2} }{(2.8*10^{4}) ^{2} *6.67*10^{-11} } \\M=6.27*10^{23}kg

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1. An object (m = 500 g) with an initial speed of 0.2 m/s collides with another object (m = 1.5 kg) which was at rest before the
Anettt [7]

Answer:

Explanation:

1 )

We shall apply conservation of momentum law to solve the problem.

mv = ( M +m) V , m and M are masses of small and large object , v is the velocity of small object before collision and V is the velocity of both the objects together after collision .

.5 x .2 = (1.5 + .5)V

V = .05 m /s

2 ) We shall use formula for velocity of object after elastic collision as follows

v₁ = \frac{(m_1-m_2)}{(m_1+m_2)} u_1+\frac{2m_2u_2}{(m_1+m_2)}

m₁ and m₂ are masses of first and second object u₁ and u₂ are their initial velocity and v₁ and v₂ are their final velocity.

Putting the values

= \frac{(200-1000)}{(1000+200)} \times 1 +\frac{2 \times1000\times0}{(1000+200)}

= - .66 m /s

Since the sign is negative so it will be in opposite direction .

4 0
3 years ago
A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s.
SVEN [57.7K]

Answer:

a) Knowns, initial speed v_{i}=13.0 m/s, final speed v_{f}=0 m/s and gravity due it is a constant g=9.8m/s^{2}

b) The maximum high reached by the dolphin is y_{max}=8.62 m

c) Total time is t=2.65s

Explanation:

a) First of all the initial speed is given at the start of the problem, gravity is constant and final speed is known any object thrown straight up reaches its max high at 0m/s speed.

b) Second, now that we know final speed we use v_{f} =v_{i}-gt, as we clear for t=\frac{v_{i}-v_{f} }{g}=\frac{20.0m/s}{9.8m/s^{2} }=1.32 s.

Then we use y=v_{i}t-\frac{1}{2} gt^{2}=(20.0m/s)(1.32s)-\frac{1}{2} (9.8m/s^{2} ) (1.32s)^{2}  =8.62m

c)Third, finally we can use y=v_{i}t-\frac{1}{2} gt^{2}, as we know y=0m when the dolphin fall into the water again and v_{i} =13.0m/s, then we have 0=(13m/s)t-\frac{1}{2} (9.8m/s^{2}  )t^{2} is a quadratic form 0=t(13.0-4.9t) so we have t_{i}=0s and t_{f}=\frac{13}{4.90}  =2.65s

6 0
3 years ago
An inventor develops a stationary cycling device by which an individual, while pedaling, can convert all of the energy expended
Eddi Din [679]

Answer:

Emec = 94050 [J]

Explanation:

In order to solve this problem, we must understand that all thermal energy is converted into mechanical energy.

The thermal energy can be calculated by means of the following expression.

Q=m*C_{p}*(T_{final}-T_{initial})

where:

Q = heat [J]

Cp = specific heat of water = 4186 [J/kg*°C]

m = mass = 300 [g] = 0.3 [kg]

T_final = 95 [°C]

T_initial = 20 [°C]

Now we can calculate the heat, replacing the given values:

Q=0.3*4180*(95-20)\\Q= 94050[J]

Since all this energy must come from the mechanical energy delivered by the exercise bike, and no energy is lost during the process, the mechanical energy must be equal to the thermal energy.

Q=E_{mec}\\E_{mec}=94050[J]

4 0
2 years ago
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