Answer:
a. 141.3 kg/s b. 5.49 m/s² c. i. 104228.9 N ii. 8.53 m/s² d. i. 97305.2 N ii. 9.84 m/s²
Explanation:
a. What must be the fuel/oxidizer consumption rate (in kg s1)?
The thrust T = Rv where R = mass consumption rate and v = velocity of rocket. Since T = 195000 N and v = 1380 m/s,
R = T/v = 195000 N/1380 m/s = 141.3 kg/s
b. If the initial weight of the rocket is 125000 N, what is its initial acceleration?
We also know that thrust T - W = ma since the rocket has to move against gravity. where M = mass of rocket = W/g = 125000 N/9.8m/s² = 12755.1 kg, W = weight of rocket = 125000 N, a = acceleration of rocket and T = thrust = 195000 N.
So, T - W = Ma
195000 N - 125000 N = (12755.1 kg)a
70000 N = ma
a = 70000 N/12755.1 kg = 5.49 m/s²
c. What are the weight and acceleration of the rocket at t 15.0 s after ignition?
We know that the loss in mass ΔM = mass consumption rate × time = Rt. Since R = 141.3 kg/s and t = 15 s,
ΔM = 141.3 kg/s × 15 = 2119.5 kg
The new mass is thus M = M - ΔM = 12755.1 kg - 2119.5 kg = 10635.6 kg
i.The weight after 15 seconds is thus W' = M'g = 10635.6 kg × 9.8m/s² = 104228.9 N
ii. Since T - W' = M'a. where M' is our new mass and a our new acceleration,
a = (T - W')/M'
= (195000 N - 104228.9 N)/10635.6 kg
= 90771.1 N/10635.6 kg
= 8.53 m/s²
d. What are the weight and acceleration of the rocket at 20.0 s after ignition?
We know that the loss in mass ΔM" = mass consumption rate × time = Rt. Since R = 141.3 kg/s and t = 20 s,
ΔM" = 141.3 kg/s × 20 = 2826 kg
The new mass is thus M" = M - ΔM" = 12755.1 kg - 2826 kg = 9929.1 kg
i. The weight after 20 seconds is thus W" = M"g = 9929.1 kg × 9.8m/s² = 97305.2 N
ii. Since T - W" = M"a. where M" is our new mass and a our new acceleration,
a = (T - W")/M"
= (195000 N - 97305.2 N)/9929.1 kg
= 97694.8 N/9929.1 kg
= 9.84 m/s²
