Physics problems Classical Mechanics and Gravitation

[Superdreamer]

Hi i was wondering if anyone could help me with the following problems please,I'm a bit confused!

Q1. A 9.4 kg projectile is fired vertically upwards. Air drag dissipates
68 kJ during its ascent. How much higher would it have gone were air drag
negligible?

Here I used the formula mgh and worked out the height to be 738.17m.Is this right If not what formula and method should I use?

q2 Suppose the Sun were to run out of nuclear fuel and collapse to form a
white dwarf star, with a radius equal to that of the Earth (6.4 x 10 6 m).
Assuming no mass loss, what would then be the Sun’s new rotational
period. Assume that both the Sun and the white dwarf are uniform solid
spheres. (The period of the sun is currently about 25 days. The moment of
inertia of a sphere is 5
r M 2 2
and the solar radius is 6.7 x 10 8 m.)

Completely lost on this q don't know where to start?

Q3 The Martian satellite Phobos travels in an approximately circular orbit of
radius r = 9.4 x 10 6 m with a period T of 459 minutes. Calculate the mass of
Mars from this information.

I used keplers 3rd law here Gm=4piR^2/T^2 and found the mass to be 6.43 x10^-13 is this the correct way for doing this?

 

[Andrew Mason]

Hi i was wondering if anyone could help me with the following problems please,I'm a bit confused!

Q1. A 9.4 kg projectile is fired vertically upwards. Air drag dissipates
68 kJ during its ascent. How much higher would it have gone were air drag
negligible?

Here I used the formula mgh and worked out the height to be 738.17m.Is this right If not what formula and method should I use?

Your answer is correct.

q2 Suppose the Sun were to run out of nuclear fuel and collapse to form a white dwarf star, with a radius equal to that of the Earth (6.4 x 10 6 m).
Assuming no mass loss, what would then be the Sun’s new rotational
period. Assume that both the Sun and the white dwarf are uniform solid
spheres. (The period of the sun is currently about 25 days. The moment of
inertia of a sphere is 5
r M 2 2
and the solar radius is 6.7 x 10 8 m.)

Angular momentum must be conserved in this scenario:
$$L = I\omega = L' = I'\omega'$$
where:
[tex]I = \frac{2mr^2}{5}[/itex]<br /> <br /> Since m remains constant, $\omega$ must change as r changes. Work it out.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Q3 The Martian satellite Phobos travels in an approximately circular orbit of radius r = 9.4 x 10 6 m with a period T of 459 minutes. Calculate the mass of Mars from this information.<br /> <br /> I used keplers 3rd law here Gm=4piR^2/T^2 and found the mass to be 6.43 x10^-13 is this the correct way for doing this? </div> </div> </blockquote>I don't think you have Kepler's third law stated correctly. <br /> <br /> The centripetal acceleration has to be supplied by gravity. The centripetal acceleration for Phobos is: $a_c = \omega^2 r$. The gravitational acceleration is: <br /> <br /> $$a_g = \frac{GM_{mars}}{r^2}$$<br /> <br /> Equate the two and work out $M_{mars}$ from that.<br /> <br /> AM[/tex]