Question

How much work is required to lift a 2000-kg satellite from the surface of 7x10^6 the earth to an altitude of m?

Answer 1

Work done, W = 1.37 × 10¹¹ J

Step-by-step explanation:

It is given that,

Mass of a satellite, m = 2000 kg

Height from the surface of earth,
`d=7* 10^6\ m`

Work done is given by :

`W=F.d`

`W=mgd`

`W=2000* 9.8* 7* 10^6`

`W=1.37* 10^(11)\ J`

Hence, this is the required solution.

Answer 2

The correct text of the problem is: "How much work is required to lift a 2000-kg satellite from the surface of the earth to an altitude of 7x10^6 m?"

Solution:The work needed to lift the satellite from the surface of Earth to an altitude h is equal to the increase in gravitational potential energy of the satellite moving from the surface of Earth to altitude h. This variation of gravitational potential energy is given by:

`\Delta U=mg\Delta h`
where m is the mass of the satellite, g is the gravitational acceleration and dh is the variation of altitude. The work is equal to this variation of energy:

`W=\Delta U`
The mass of the satellite is m=2000 kg while the variation of altitude is

`h=7 \cdot 10^6 m`
so we can plug these data into the equation to calculate the variation of gravitational potential energy, which is equal to the work done on the satellite:
`W=\Delta U=(2000 kg)(9.81 m/s^2)(7\cdot 10^6 m)=1.4\cdot 10^(11) J`