If a rocket with a mass of 2900 tons vertically accelerates at a rate of # 2/9 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 6 seconds?

Question

Leo Abeyta · Accepted Answer

First work out what force the rocket is exerting to accelerate. Then use: Power = Force x Velocity.

The rocket's power is approximately 35.9 MW after 6 seconds.

The first step is to find what resultant upward force needs to be exerted by the rocket to make it accelerate upwards at #2/9 m s^-2#, which we shall denote as #a_r#. The resultant force #F# is equal to the upward force provided by the rocket's motor, #F_r#, minus the force of gravity #F_g# Downward forces - upward forces equals the resultant upward force. #F = F_r - F_g# Rearrange to make #F_r# the subject: #F_r = F + F_g# Newton's 2nd law tells us that: F = m a The question tells us the upward acceleration is: #a_r=2/9 m s^-2#, which is provided by the resultant force, so: #F = m_r times a_r# where #m_r# is the rocket's mass. #F_g = m_r times text(acceleration due to gravity) = m_r times g# Now: #F_r =m_r times a_r + m_r times g = m_r(a_r + g)# Now that we have a force expression, let's talk about the power: Power = Force x Velocity Velocity = acceleration x time Power = #m_r(a_r + g) times (a_r times t)# Since you're from the USA, we'll refer to your tons as US tons, or short tons. #m_r = 2900 text( tons) ~= 2900 text( tons) times 907 text( kg per ton = 2630300 kg# #a_r = 2/9 m s^-2# #g ~= 10 m s^-2# (use a more accurate value if you want) t = 6 seconds Finally, putting it all together: Power #~= (2630300 kg)(92/9 m s^-2) times 2/9 m s^-2 times 6s# Power #~= (241987600/9 N) times 12/9 m s^-1# Power #~= 35850015 J s^-1 = 35850015# watts After six seconds, the rocket's power is thus roughly 35.9 MW.

Lily Adams · Answer

undefined To calculate the power exerted by the rocket, you can use the formula:

Power = Force × Velocity

First, find the force exerted by the rocket using Newton's second law:

Force = Mass × Acceleration

Then, find the velocity of the rocket using the formula for uniform acceleration:

Velocity = Initial Velocity + Acceleration × Time

Substitute the given values into the equations and solve for the power.

Given:
Mass (m) = 2900 tons = 2900000 kg
Acceleration (a) = 2/9 m/s^2
Time (t) = 6 seconds

Using Newton's second law:
Force = Mass × Acceleration

Using the formula for uniform acceleration to find velocity:
Velocity = Initial Velocity + Acceleration × Time

Since the initial velocity is not given, we assume it's zero for simplicity.

Now, solve for the force and velocity:

Force = (2900000 kg) × (2/9 m/s^2)
Force ≈ 644444.44 N

Velocity = 0 + (2/9 m/s^2) × (6 s)
Velocity ≈ 4/3 m/s

Now, calculate the power:

Power = Force × Velocity
Power ≈ (644444.44 N) × (4/3 m/s)
Power ≈ 858,592.59 Watts

So, the rocket will have to exert approximately 858,592.59 Watts of power to maintain its acceleration after 6 seconds.