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1 year ago

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In 2014, the Rosetta space probe reached the comet Churyumov Gerasimenko. Although the comet's core is actually far from spheric

al, in this problem we'll model it as a sphere with a mass of 1.0 × 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet's surface, how long would it take to hit the surface?

1 answer:

Viktor [21]1 year ago

8 0

To solve this problem we will apply the concepts related to gravity according to the Newtonian definitions. From finding this value we will use the linear motion kinematic equations to find the time. Our values are

Comet mass $M = 1.0*10^{13} kg$

Radius $r = 1.6km = 1600 m$

Rock was dropped from a height 'h' from surface = 1m

The relation for acceleration due to gravity of a body of mass 'm' with radius 'r' is

$g = \frac{GM}{R^2}$

Where G means gravitational universal constant and M the mass of the planet

$g = \frac{(6.67408*10^{-11})(1*10^{13})}{1600^2}$

$g = 2.607*10^{-4} m/s^2$

Now calculate the value of the time

$h = \frac{1}{2} gt^2$

$t = \sqrt{\frac{2h}{g}}$

$t = \sqrt{\frac{2(1)}{2.607*10^{-4}}}$

$t = 87.58s$

The time taken for the rock to reach the surface is t = 87.58s

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A car has a mass of 1600 kg. It is stuck in the snow and is being pulled out by a cable that applies a force of 7560 N due north

sergiy2304 [10]

Answer:

Acceleration of the car will be $a=0.1375m/sec^2$

Explanation:

We have given mass of the ball m = 1600 kg

Force in north direction F= 7560 N

Resistance force which opposes the movement of car $F_R=7340N$

So net force on the car $F_{net}=F-F_R=7560-7340=220N$

According to second law of motion we know that F=ma

So $220=1600\times a$

$a=0.1375m/sec^2$

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2 years ago

4. Going back to the dog whistle in question 1, what is the minimum riding speed needed to be able to hear the whistle? Remember

jeyben [28]

Answer:

The minimum riding speed relative to the whistle (stationary) to be able to hear the sound at 21.0 kHz frequency is 15.7 m/s

Explanation:

The Doppler shift equation is given as follows;

$f' = \dfrac{v - v_o}{v + v_s} \times f$

Where:

f' = Required observed frequency = 20.0 kHz

f = Real frequency = 21.0 kHz

v = Sound wave velocity = 330 m/s

$v_o$ = Observer velocity = X m/s

$v_s$ = Source velocity = 0 m/s (Assuming the source is stationary)

Which gives;

$20 = \dfrac{330- v_o}{330+0} \times 21$

330 - $v_o$ = (20/21)*330

$v_o$ = 330 - (20/21)*330 = 15.7 m/s

The minimum riding speed relative to the whistle (stationary) to be able to hear the sound at 21.0 kHz frequency = 15.7 m/s.

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1 year ago

Weddell seals make holes in sea ice so that they can swim down to forage on the ocean floor below. Measurements for one seal sho

Mariulka [41]

Answer:

B. 1 m/s

Explanation:

Metric unit conversions:

0.3 km = 300m

5 minutes = 5*60 = 300 seconds

So if a seal can reach a depth of 300m in a time of 300 seconds, its diving speed is the distance divided by time duration

v = s/t = 300/300 = 1m/s

So B is the correct answer

3 0

1 year ago

A rigid tank whose volume is unknown is divided into two parts by a partition. One side of the tank contains an ideal gas at 935

a_sh-v [17]

Answer:

2805 °C

Explanation:

If the gas in the tank behaves as ideal gas at the start and end of the process. We can use the following equation:

$P=RTn/V$

The key issue is identify the quantities (P,T, V, n) in the initial and final state, particularly the quantities that change.

In the initial situation the gas have an initial volume $V_{i}$ , temperature $T_{i}$ , and pressure $P$ ,.

And in the final situation the gas have different volume $V_{f}$ and temeperature $T_{f}$ , the same pressure $P$ ,, and the same number of moles $n$ ,.

We can write the gas ideal equation for each state:

$P=RT_{i}n/V_{i}$ and $P=RT_{f}n/V_{f}$ , as the pressure are equals in both states we can write

$RT_{i}n/V_{i} = RT_{f}n/V_{f}$

solving for $T_{f}$

$T_{f} = T_{i}/V_{i} * V_{f}$ (*)

We know $T_{i}$ = 935 °C, and that the $V_{f}$ (the complete volume of the tank) is the initial volume $V_{i}$ plus the part initially without gas which has a volume twice the size of the initial volume (read in the statement: the other side has a volume twice the size of the part containing the gas). So the final volume $V_{f}= V_{i} + 2V_{i}=3V_{i}$

Replacing in (*)

$T_{f} = 935/V_{i} * 3V_{i} = 935*3= 2805$

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1 year ago

A quadraphonic car stereo operates on electric current provided by the car's 12V battery and is connected in series. Each channe

yKpoI14uk [10]

Answer:

2.93 A

Explanation:

From Ohm's law V = IR where V = voltage = 12 V, I = current = ? and R = resistance = 4.1 Ω.

So, the current in each quadraphonic stereo circuit is I = V/R = 12 V/4.1 Ω = 2.93 A

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1 year ago