A 72.0 kg piece of a satellite left over from an explosion with zero orbital velocity in space falls from a distance of 190 above the surface of the earth down toward earth. It arrives with 29.5 Km (M="mega") kinetic energy on earth. How many MJ energy have been lost due to friction in the earth's atmosphere ? Use the exact expression for the gravitational potential energy.
What are the units of the "190" elevation from which it fell?
29.5 Km is not a measure of energy. Please copy the question more carefully
190Km *
29.5 MJ *
The gravitational potential energy change is
deltaPE = -G*M*m/R + G*M*m/(R+h)
where G is the universal gravity constant, M is the mass of the earth, m is 170 kg and R is the radius of the earth (6,378,000 m). h is the initial altitude above the Earth's surface.
This can also be written
deltaPE = -mgR + mgR[R/(R+h)]
= -mgR{1 - [1/(1 + h/R)]}
= -170kg*9.8 m/s^2*6378*10^3 m
*{1 - [1 - 1/(1 + (190/6378))]
= -1.063*10^10*0.0289 = -3.071*10^8 J
So 307 MegaJoules of gravitational PE is lost. If the kinetic energy on arrival is 29.5 mJ, the remainder has been lost due to frictkion, and converted to heat.
thank you, but for some reason its wrong
it says "Make sure you calculate with at least 3 significant digits. Express your answer using two significant figures."
The above equation is all right -- just make sure you use the right value for mass (72 kg; not 170). Also, make sure you convert the 190km into meters--therefore your calculations would be (190,000m/6.4e6m). If you do all the conversions right, you should get the right answer! Good luck.
To calculate the energy lost due to friction in the Earth's atmosphere, we need to find the difference between the initial total energy (potential energy) of the satellite and its final total energy (kinetic energy) on Earth.
Let's break down the calculation step by step:
Step 1: Calculate the initial potential energy of the satellite
The gravitational potential energy (PE) can be calculated using the formula:
PE = mgh
where m is the mass of the satellite, g is the acceleration due to gravity, and h is the height above the surface of the Earth.
In this case:
m = 72.0 kg
g = 9.8 m/s^2
h = 190 km = 190000 m
Using these values, we can calculate the initial potential energy (PE_initial):
PE_initial = m * g * h
Step 2: Calculate the final kinetic energy of the satellite on Earth
The kinetic energy (KE) can be calculated using the formula:
KE = 1/2 * mv^2
where m is the mass of the satellite and v is the velocity of the satellite.
In this case:
m = 72.0 kg
v = 29.5 km/s = 29500 m/s
Using these values, we can calculate the final kinetic energy (KE_final):
KE_final = 1/2 * m * v^2
Step 3: Calculate the energy lost due to friction
The energy lost due to friction is the difference between the initial potential energy and the final kinetic energy:
Energy_lost = PE_initial - KE_final
Step 4: Convert the result to MJ (mega-joules)
The given value is in joules, but we need to convert it to mega-joules by dividing by 1 million:
Energy_lost_in_MJ = Energy_lost / 1,000,000
Now, let's plug in the values and calculate:
m = 72.0 kg
g = 9.8 m/s^2
h = 190,000 m
v = 29,500 m/s
PE_initial = m * g * h
PE_initial = 72.0 kg * 9.8 m/s^2 * 190,000 m
KE_final = 1/2 * m * v^2
KE_final = 1/2 * 72.0 kg * (29,500 m/s)^2
Energy_lost = PE_initial - KE_final
Finally, convert the energy lost to MJ:
Energy_lost_in_MJ = Energy_lost / 1,000,000
By performing these calculations, you will find the amount of energy lost due to friction in the Earth's atmosphere.