A rocket with mass of 60,000 kg is placed on a launching platform verticlly. its engine is started and the rocket gives out gas at rate of 50kgs^-1 with a speed of 5000ms^-1
a) calculate the up trust force caused by the gas.
b) can the rocket be launched at this moment?
force = change in momentum/time
= (50 kg * 5000 m/s) /s = 250,000 Newtons thrust
weight = m g = 60,000*9.81 = 588,600 N
no way
To calculate the upward thrust force caused by the gas, we need to apply the principle of conservation of momentum.
a) The mass of gas expelled per second is given as 50 kg/s, and the speed of the gas expelled is given as 5000 m/s. The change in momentum of the gas can be calculated as:
Change in momentum = mass x velocity = 50 kg/s x 5000 m/s = 250,000 kg·m/s
According to the principle of conservation of momentum, the change in momentum of the rocket must be equal and opposite to the change in momentum of the gas. Therefore, the upward thrust force can be calculated as:
Upward thrust force = Change in momentum / Time taken
However, the time taken is not provided in the given information. Without the time taken, we cannot calculate the upward thrust force accurately.
b) To determine if the rocket can be launched at this moment, we need to consider the gravitational force acting on the rocket. The weight of the rocket can be calculated using the formula:
Weight = mass x gravitational acceleration
Assuming the gravitational acceleration as 9.8 m/s^2, the weight of the rocket is:
Weight = 60,000 kg x 9.8 m/s^2 = 588,000 N
If the upward thrust force exerted by the gas is greater than or equal to the weight of the rocket, then the rocket can be launched. If the upward thrust force is lesser than the weight, the rocket cannot be launched. However, without the accurate calculation of upward thrust force, we cannot determine for sure if the rocket can be launched at this moment.