Urgent! Space II Help! (1 Viewer)

[x.Exhaust.x]

1. Two planets X and y are located in a galaxy 1009 light years from Earth. Planet X has twice the radius of Y, but is 8 times the mass of Y. COmpare the escape velocities of both planets

2. From the top of his house Sir Isaac Newton throws several apples horizontally at various speeds. Two of these apple trajectories include a 20m vertical height, with 25m horizontal for apple A and an unknown horizontal for apple B.

a) At what velocity was apple A projected?
b) If it took apple B took 2 secs to hit the ground, and it landed twice as far apple A, at what velocity was it projected at?

3. A 30kg object, A, was fired from a cannon in projectile motion. WHen the projectile was at its maximum height of 25m, its speed was 20ms^-1. An identical object B, was attached to a mechanical arm and moved at a constant speed of 20ms^-1 in a vertical half circle. The length of the arm was 25m.

a) Calculate the force acting on object A at its max. height.
b) Calculate the time it would take object A to reach the ground from its position of max. height.
c) Describe and compare the vertical forces acting on objects A and B at their maximum heights.

Thanks in advance.

 

[dolbinau]

Can't be bothered to do anything else, but 1, I hope is right

1. Escape velocity is twice as big on planet X than planet Y (use V=(2GM/R)^1/2) ) formula.

 

[Graceofgod]

Ok, here we go =S

1) v = root[2GM/r]
v(X) = root[2G(8M)/2r]
v(Y) = root[2GM/r]
cancelling out constants:
v(X) = root(8/2)
v(Y) = root(1)
X = 2x larger escape velocity than Y

2a) Vertical:
s = 20 u = 0 a = 9.8 t = ?
s = ut + 1/2(at^2)
20 = 1/2(9.8*t^2)
t^2 = 4.0816326...
t = 2.02 seconds (2d.p.)

Horizontal:
s = ut
25 = 2.02u
u = 12.376 m/s (3d.p.)

b)
s = ut
50 = 2u
u = 25m/s

3) Not so sure about this one, correct me if I am wrong:
a) There is no acceleration horizontally so no force (ignoring air resistance )
F = ma
m = 30 a = 9.8
F = 294 N

b) s = 25 u = 0 a = 9.8 t = ?
s = ut + 1/2(at^2)
25 = 1/2(9.8*t^2)
t = 2.26 m/s (2d.p.)

c) Vertical force on A = 294 N. Vertical force on B = 0 (downward force canceled out by upward force of arm, I think).

 

[Glenjamin]

2a)

Delta Y = Uyt + .5ayt^2
20 = 4.9t^2
2.02 = t

therefore Delta x = Uxt

25 = Ux (2.02)
12.376 = Ux

 

[x.Exhaust.x]

Thanks!

Two more questions:

1. Show that using simple maths that if c is invariant then space and time must be relative.

2. John says that his clock reads 12:00:00 when two bolts of lightning strike. Mike on the other hand says his clocks reads 12:00:02. Both were in their own inertial reference frames. Discuss why they obtain different answers.

I thought it was through the relativity of simultaneity, but a friend told me there's more to it.

 

[Mind-Revolution]

Thanks!

Two more questions:

1. Show that using simple maths that if c is invariant then space and time must be relative.

2. John says that his clock reads 12:00:00 when two bolts of lightning strike. Mike on the other hand says his clocks reads 12:00:02. Both were in their own inertial reference frames. Discuss why they obtain different answers.

I thought it was through the relativity of simultaneity, but a friend told me there's more to it.

1. Well, c is the speed of light, and basically velocity = distance / time (v = d / t). Then, if c (v) is to be constant, then distance (space) and time (obviously time) must vary / be relative to maintain the constant speed of light.



2. Well, perhaps time dilation is a cause. Inertial = rest / constant velocity.

If both are in inertial frames, then one be at rest / other at constant velocity.

John says - 12:00:00. Mike says - 12:00:02.

It is likely, John is travelling at a high speed (a relativistic speed), and in his frame records the event at 12:00:00 (the proper time of the event).

However, Mike is at rest, and time dilation occurs (where time in John's moving frame appears to go slower relative to the stationary observer - Mike, thus why John records a smaller time value - 12:00:00).

So, while John records the event to occur at 12:00:00, Mike observes the event at 12:00:02 as he observes a dilated time (time lengthens / dilates / takes longer, and thus accounts for his higher recorded value of 12:00:02 for the event).

The stationary person (Mike) always records a higher value than what the moving observer records (John).

Hopefully...