Video Transcript
The gravitational field strength of a planet becomes weaker as the distance from the planet’s surface increases. Several thousand kilometers above a planet, its gravitational field strength is 2.4 newtons per kilogram. What force in kilonewtons towards the planet’s surface is experienced by a spacecraft with a mass of 25000 kilograms?
The question wants us to consider a planet. And we’re told that as the distance from the planet’s surface increases, the gravitational field strength of the planet becomes weaker. Now this fact is a consequence of Newton’s law of gravitation, and it would hold true for any planet or in fact for any object that has a mass. For the particular planet in this question, we’re told that at some specific height of the order of several thousand kilometers above its surface, the gravitational field strength of this planet is 2.4 newtons per kilogram. Let’s label the gravitational field strength at this height as 𝑔.
We’re being asked to consider a spacecraft at this height above the planet’s surface, so that’s spacecraft in this gravitational field with the strength of 2.4 newtons per kilogram. Let’s suppose that this here is our spacecraft. And while we don’t know the height that this spacecraft is above the planet’s surface, we do know the value of the gravitational field strength at this height, whatever that height is. We also know that the mass of the spacecraft is 25000 kilograms. We’ll label this mass as 𝑚. We’re being asked to work out the force towards the planet’s surface that the spacecraft experiences. We’ve labeled this force in our diagram as 𝑤, which stands for weight, because the force experienced by the spacecraft is equal to the spacecraft’s weight in this gravitational field.
We can recall that if we’ve got an object with a mass 𝑚 in a gravitational field with strength 𝑔, then the weight 𝑤 of the object in this field is equal to 𝑚 multiplied by 𝑔. Now, in our case, this quantity 𝑤 is the force toward the planet’s surface experienced by the spacecraft, which is what we’re asked to work out. So, we know that 𝑤 is equal to 𝑚 multiplied by 𝑔. And in this situation, we already know the values for the mass 𝑚 and the gravitational field strength 𝑔. This means we can go straight ahead and take these two values and substitute them into this equation to calculate the weight 𝑤. When we do this, we find that 𝑤 is equal to 25000 kilograms, that’s the mass 𝑚 of the spacecraft, multiplied by 2.4 newtons per kilogram, that’s the gravitational field strength 𝑔 at the height the spacecraft is above the planet’s surface.
Looking at the units on the right-hand side, we’ve got a mass in kilograms and a gravitational field strength in newtons per kilogram. When we multiply these two quantities together, the kilograms and the per kilogram will cancel each other out. And we’re left with a weight force in units of newtons. Then evaluating this expression, we get a result of 60000 newtons. We can notice though that the question wants this force given in units of kilonewtons.
Let’s recall that one kilonewton is equal to 1000 newtons. This means that to convert from units of newtons to units of kilonewtons, we need to divide by a factor of 1000. So then in units of kilonewtons 𝑤 must be equal to 60000 divided by 1000 kilonewtons. This works out as 60 kilonewtons. Our answer then is that the force toward the planet’s surface experienced by the spacecraft is equal to 60 kilonewtons.
