a 55 kg satellite is in circular orbit earth with an orbital radius of 7.4 x 10^6 m . determine the satellite’s
a)kinetic energy
b)gravitational potential energy
c)total energy
d)binding energy
a) set mv^2/r = GMm/r^2
v = sqrt(GM/r) M = 5.98e24 r = 7.4e6 + radius of earth which is something like 6300km. You'll have to look it up.
b) PE = mgh h is the r you used in part a
c) add 'em up
d) not familiar with the term
To calculate the satellite's kinetic energy, gravitational potential energy, total energy, and binding energy, we need to use the following equations:
a) Kinetic Energy (KE) = (1/2) * mass * velocity^2
b) Gravitational Potential Energy (PE) = mass * gravitational acceleration * distance
c) Total Energy (TE) = KE + PE
d) Binding Energy (BE) = TE / mass
Let's break down each calculation step by step:
a) Kinetic Energy (KE):
The satellite is in circular orbit, so its velocity can be found using the formula v = (G * M) / r, where G is the gravitational constant (6.67 x 10^-11 N(m/kg)^2), M is Earth's mass (5.97 x 10^24 kg), and r is the orbital radius.
Substituting the values, we get:
v = (6.67 x 10^-11 N(m/kg)^2 * 5.97 x 10^24 kg) / (7.4 x 10^6 m)
Compute the equation to find the velocity, v.
Once you have the velocity, substitute it into the kinetic energy formula to find the final answer.
b) Gravitational Potential Energy (PE):
The gravitational potential energy can be calculated using the formula mentioned earlier: PE = mass * gravitational acceleration * distance.
Substitute the given values into the equation and solve for PE.
c) Total Energy (TE):
Total energy is the sum of kinetic energy (KE) and gravitational potential energy (PE), so add the results from part a and part b together to find TE.
d) Binding Energy (BE):
Binding energy is the total energy divided by the mass of the satellite. Divide TE from part c by the given mass to get BE.
By following these steps and substituting the given values into the appropriate equations, you will be able to calculate the satellite's kinetic energy, gravitational potential energy, total energy, and binding energy.