A rocket blasts off from rest and attains a speed of 49 m/s in 16 s. An astronaut has a mass of 56.3 kg. What is the astronaut's apparent weight during take off?
a = (final velocity -initial velocity)/time
a = 49/16 m/s^2
weight = m g + m(49/16)
To find the astronaut's apparent weight during takeoff, we need to consider the force acting on the astronaut.
The apparent weight of an object is the force exerted on it by a supporting surface. On the surface of the Earth, the apparent weight is due to two forces: the gravitational force and the force exerted by the ground.
During takeoff, the rocket generates an upward force (thrust) that propels the astronaut and the rocket upward. This thrust counteracts the force of gravity and reduces the apparent weight of the astronaut.
To find the astronaut's apparent weight, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force acting on the astronaut is the difference between the gravitational force (mg) and the force of thrust (T). So:
Net force = Thrust - Gravitational force
Using the equation for the net force:
ma = T - mg
Where:
m = mass of the astronaut (56.3 kg)
a = acceleration (which can be found using the given change in speed and time)
g = acceleration due to gravity (approximately 9.8 m/s²)
The change in velocity (Δv) is given as 49 m/s, and the time taken (Δt) is given as 16 s. Therefore, the acceleration can be calculated as:
a = Δv / Δt = 49 m/s / 16 s = 3.06 m/s²
Now we can substitute the values into the equation:
(56.3 kg) * (3.06 m/s²) = T - (56.3 kg) * (9.8 m/s²)
Solving for T:
T = (56.3 kg) * (3.06 m/s²) + (56.3 kg) * (9.8 m/s²)
T ≈ 1730.63 N
Therefore, the thrust exerted by the rocket is approximately 1730.63 N.
Finally, to find the astronaut's apparent weight during takeoff, we need to subtract the force of thrust from the gravitational force:
Apparent weight = Gravitational force - Thrust
Apparent weight = (56.3 kg) * (9.8 m/s²) - (1730.63 N)
Calculating the value:
Apparent weight ≈ 552.94 N.
Therefore, the astronaut's apparent weight during takeoff is approximately 552.94 N.
To determine the astronaut's apparent weight during takeoff, we need to calculate the net force acting on the astronaut.
Step 1: Calculate the astronaut's weight:
The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
Given:
Mass of the astronaut (m) = 56.3 kg
Gravitational acceleration (g) on Earth is approximately 9.8 m/s^2.
Weight of the astronaut = 56.3 kg × 9.8 m/s^2
Step 2: Calculate the net force acting on the astronaut:
Since the rocket is accelerating, there is an additional force acting on the astronaut apart from gravity. This additional force can be calculated using Newton's second law of motion:
Net force = mass × acceleration
Given:
Acceleration (a) = change in velocity / time
Change in velocity (Δv) = final velocity - initial velocity = 49 m/s - 0 m/s = 49 m/s
Time (t) = 16 s
Acceleration (a) = 49 m/s / 16 s
Net force = 56.3 kg × (49 m/s / 16 s)
Step 3: Calculate the apparent weight:
The apparent weight is the force experienced by the astronaut, which is equal to the net force acting on the astronaut.
Apparent weight = net force
Apparent weight = 56.3 kg × (49 m/s) / (16 s)