A rocket blasts off from rest and attains a speed of 59.4 m/s in 14.1 s. An astronaut has a mass of 66.7 kg. What is the astronaut's apparent weight during takeoff?
To find the astronaut's apparent weight during takeoff, we need to first calculate the net force acting on the astronaut. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The acceleration of the astronaut can be found using the formula:
acceleration = change in velocity / time
In this case, the change in velocity is the final velocity (59.4 m/s) minus the initial velocity (0 m/s), and the time is 14.1 s.
acceleration = (59.4 m/s - 0 m/s) / 14.1 s
acceleration = 59.4 m/s / 14.1 s
acceleration ≈ 4.22 m/s²
Now that we know the acceleration of the astronaut, we can calculate the net force using the formula:
net force = mass * acceleration
In this case, the mass of the astronaut is given as 66.7 kg.
net force = 66.7 kg * 4.22 m/s²
net force ≈ 280.9 N
The apparent weight of an object is the force exerted on it due to gravity. This force is equal to the mass of the object multiplied by the acceleration due to gravity (9.8 m/s²).
apparent weight = mass * acceleration due to gravity
apparent weight = 66.7 kg * 9.8 m/s²
apparent weight ≈ 652.7 N
Therefore, the astronaut's apparent weight during takeoff is approximately 652.7 Newtons.