Question

In: Physics

Find the energy necessary to put 5 kg , initially at rest on Earth's surface, into...

Find the energy necessary to put 5 kg , initially at rest on Earth's surface, into geosynchronous orbit.

Solutions

Expert Solution

The energy necessary to put a 5 kg mass into the gs orbit can be calculated as follows:

The energy of the mass m in such an orbit is
E = P.E. + K.E.
...= GM m / (r - R) + m v^2 /2 ........(1)
v is the linear velocity of the mass m in gs orbit of radius r
This given by ,
GM m / r^2 = m v^2 / r
v^2 = GM / r ..........................(2)
Put this value in (1)
E = GM m / (r - R) + GM m / 2 r = ........(3)

For a gs orbit the angular velocity of the mass m must be same as that of the earth's rotation on its axis.
ω = 2π / T = 2 π / 24 x 3600 = 7.272 x10^-5 rad/s

From (2),
GM / r = r^2 ω^2
r^3 = GM / ω^2
G = 6.67x10^-11
M = 6x10^24 kg
That gives r , the radius of the gs orbit from the center of the earth, as
r = 4.23x10^7 m

R = 6.4 x10^6 m (radius of the earth)
r - R = (42.3 - 6.4)x10^6 = 35.9 x10^6 m

From (3) you can obtain the energy of the mass m = 5 kg as ,
E = 39.69 x 10^6 J

This is the minimum energy required to put the object of mass 5 kg on the earth surface into a gs orbit.


Related Solutions

Find the energy necessary to put 7 kg , initially at rest on Earth's surface, into...
Find the energy necessary to put 7 kg , initially at rest on Earth's surface, into geostationary orbit.
A 0.300-kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200-kg...
A 0.300-kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200-kg puck moving initially along the x axis with a speed of 2.00 m/s. After the collision, the 0.200- kg puck has a speed of 1.00 m/s at an angle of θ = 53.0° to the positive x axis. (a) Determine the velocity of the 0.300-kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision. and please explain
A 0.300-kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200-kg...
A 0.300-kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.200-kg puck moving initially along the x axis with a speed of 2.00 m/s. After the collision, the 0.200- kg puck has a speed of 1.00 m/s at an angle of θ = 53.0° to the positive x axis. (a) Determine the velocity of the 0.300-kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision. (4 points)
A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg...
A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 9.0 m/s. After the collision, the 0.20-kg puck has a speed of 5.4 m/s at an angle of θ = 53° to the positive x-axis. a)Determine the velocity of the 0.30-kg puck after the collision. magnitude-? direction-? (from the positive X-axis) (b) Find the fraction of kinetic energy lost in the collision.
A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg...
A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 8.6 m/s. After the collision, the 0.20-kg puck has a speed of 5.2 m/s at an angle of θ = 53° to the positive x-axis. (a) Determine the velocity of the 0.30-kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision.
A 0.478 kg puck, initially at rest on a horizontal, frictionless surface, is struck by a...
A 0.478 kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.129 kg puck moving initially along the x axis with a speed of 2.19 m/s. After the collision, the 0.129 kg puck has a speed of 1.19 m/s at an angle of 29◦ to the positive x axis. Determine the magnitude of the velocity of the 0.478 kg puck after the collision. Answer in units of m/s.
A 0.30 kg puck, initially at rest on a frictionless horizontal surface, is struck by a...
A 0.30 kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20 kg puck that is initially moving along the x axis with a velocity of 2.4 m/s. After the collision, the 0.20 kg puck has a speed of 0.8 m/s at an angle of θ = 53° to the positive x axis. (a) Determine the velocity of the 0.30 kg puck after the collision. _ at _ ° from +x axis (b) This was...
A 5.0 kg mass is initially at rest on a horizontal frictionless surface when a horizontal...
A 5.0 kg mass is initially at rest on a horizontal frictionless surface when a horizontal force along an x axis is applied to the block. The force is given by ? ⃗(?) = (6.0?2 − 2?3)?̂, where the force in in newtons, x is in meters, and the initial position of the block is x = 0. (a) What is the work done in moving the block from x = 1.0 m to x = 3.0 m? (b) What...
A block of mass 5 kg is sitting on a frictionless surface. The block initially has...
A block of mass 5 kg is sitting on a frictionless surface. The block initially has a velocity of 3 m/s. A force of 9 N is applied for 2 s.   What is the Initial momentum of the block? kg m/s Tries 0/2 What is the Initial Kinetic Energy of the block? J Tries 0/2 What is the change in momentum of the block?   Kg m/s Tries 0/2 What is the final momentum of the block? kg m/s Tries 0/2...
Block B is initially at rest. Then block A slides on the smooth surface to the...
Block B is initially at rest. Then block A slides on the smooth surface to the right and collides with block B with a velocity vAvA. Consider three following collision cases where: i) elastic impact; ii ) perfectly plastic impact; iii ) e = 0.5. Just after the collision, rank these three cases where the relative velocitiy of B with respect to A is from largest to smallest magnitude.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT