Video Transcript
Calculate the mass of the Falcon 9
rocket made by SpaceX given that its engines have a thrust of 7150 kilonewtons at
sea level, which accelerates the rocket upwards with an acceleration of 3.2 meters
per second squared. Assume that gravitational
acceleration, 𝑔, is constant and equal to 9.8 meters per second squared.
In this question, we are asked to
calculate the mass of a rocket given the value of its acceleration and the thrust
from its engines.
Before we do anything else, let’s
draw a quick diagram to help us visualize the forces that act on the rocket at the
instant when it leaves the ground. We are told that the engines have a
thrust of 7150 kilonewtons. The thrust is the upward force that
is exerted on the rocket by its engines when it burns fuel. So, we can represent this thrust as
an arrow pointing upwards. We’ll label it capital 𝑇 for
thrust. But there is another force that we
need to consider: the weight of the rocket, which acts vertically downwards. Let’s draw this as a downwards
arrow, labeled 𝑊 for weight.
Now that we’ve thought about the
forces acting on the rocket, we’re ready to start some calculations. Recall Newton’s second law of
motion. Newton’s second law tells us that
the net force acting on an object is equal to the mass of the object multiplied by
the object’s acceleration. In this case of this rocket, we’re
only interested in its upwards motion, since that’s the direction we’re told it
accelerates in. So we need to find the net upwards
force on the rocket. The net upwards force that acts on
the rocket is simply equal to the thrust, which pushes the rocket upwards, minus the
weight, which pulls the rocket down. So 𝐹 net is equal to 𝑇 minus
𝑊.
So far, this isn’t very helpful
because we don’t know the value of the weight of the rocket. However, recall that weight is
given by the formula 𝑊 equals 𝑚𝑔. The weight of an object is equal to
the mass of the object multiplied by the acceleration due to gravity that the object
experiences. If we substitute this in, we see
that 𝐹 net is equal to 𝑇 minus 𝑚𝑔. If we now substitute this
expression for 𝐹 net into Newton’s second law, we find that 𝑇 minus 𝑚𝑔 equals
𝑚𝑎.
To find the mass of the rocket, we
simply need to rearrange this equation to make 𝑚 the subject. To make 𝑚 the subject, we start by
adding 𝑚𝑔 to both sides of the equation to get 𝑇 is equal to 𝑚𝑎 plus 𝑚𝑔. Then, we factorize the right-hand
side to get 𝑇 is equal to 𝑚 multiplied by 𝑎 plus 𝑔. Then, we simply divide both sides
by 𝑎 plus 𝑔 to get 𝑚 is equal to 𝑇 divided by 𝑎 plus 𝑔.
Now all that left is to substitute
the values we’ve been given. We’re told that the thrust, 𝑇, is
equal to 7150 kilonewtons. Be careful of the units here. We’ve been given this value in
units of kilonewtons when really we need it in newtons. To convert from kilonewtons to
newtons, we simply multiply by 1000. So, 7150 kilonewtons equals 7150
multiplied by 1000 newtons.
We’re also told that the
acceleration of the rocket, 𝑎, is equal to 3.2 meters per second squared and the
acceleration due to gravity, 𝑔, is equal to 9.8 meters per second squared. Substituting in these values, we
find that the mass of the rocket is equal to 7150 multiplied by 1000 newtons divided
by 3.2 meters per second squared plus 9.8 meters per second squared. Completing this calculation, we
find that 𝑚 equals 550000 kilograms.
So the answer to this question is
that the Falcon 9 rocket has a mass of 550000 kilograms.
