A 70.0-kg astronaut pushes to the left on a spacecraft with a force in "gravity-free" space. The spacecraft has a total mass of 1.0 × 104 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36 m/s2.
Determine the magnitude of the acceleration of the spacecraft.
newtons 2nd law states F =m*A
Astronaut: F = 70*0.36 = 25.2 N
Spacecraft: 25.2 = 10000 * a
a = 25.2 / 10^4 m/s/s = 25.2*10^-4 = 0.00252m/s/s in a leftward direction
Well, this astronaut seems to be quite the rocket scientist! Let's calculate the magnitude of the acceleration of the spacecraft.
First, we need to use Newton's second law, 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 is the force applied by the astronaut, and the object is the spacecraft.
The force applied by the astronaut can be calculated using his mass and acceleration, and we can assume that there are no other external forces acting on the spacecraft. So, the force applied by the astronaut is given by:
Force = Mass x Acceleration
Force = 70.0 kg x 0.36 m/s^2
That gives us a force of 25.2 N.
Now, we can determine the acceleration of the spacecraft. Since the net force acting on the spacecraft is equal to the force applied by the astronaut, we can rearrange Newton's second law to solve for acceleration:
Acceleration = Net Force / Mass of the spacecraft
Acceleration = 25.2 N / (1.0 x 10^4 kg)
Plug those numbers into your calculator, and you'll find that the magnitude of the acceleration of the spacecraft is approximately 0.00252 m/s^2.
So, to sum it up, the magnitude of the acceleration of the spacecraft is about 0.00252 m/s^2. It seems like this astronaut's push didn't quite push the spacecraft to Infinity and beyond!
To determine the magnitude of the acceleration of the spacecraft, we'll use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In this scenario, the astronaut is pushing to the left on the spacecraft, causing the spacecraft to accelerate to the right. The force exerted by the astronaut on the spacecraft is the action force, and the force exerted by the spacecraft on the astronaut is the reaction force.
According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration. So, we can use this formula to calculate the force exerted by the astronaut on the spacecraft:
Force = Mass × Acceleration
The mass of the astronaut is given as 70.0 kg, and the acceleration of the astronaut to the right is given as 0.36 m/s^2. Substituting these values into the formula, we have:
Force = 70.0 kg × 0.36 m/s^2
Force = 25.2 N
Since the astronaut is pushing to the left, the force exerted by the spacecraft on the astronaut is equal in magnitude but opposite in direction. So, the force exerted by the spacecraft on the astronaut is also 25.2 N.
To determine the magnitude of the acceleration of the spacecraft, we can use the same formula, but this time with the mass of the spacecraft (1.0 × 10^4 kg) and the force exerted by the spacecraft on the astronaut (25.2 N):
Force = Mass × Acceleration
25.2 N = (1.0 × 10^4) kg × Acceleration
To find the acceleration, we rearrange the equation:
Acceleration = 25.2 N / (1.0 × 10^4 kg)
Acceleration ≈ 0.00252 m/s^2
Therefore, the magnitude of the acceleration of the spacecraft is approximately 0.00252 m/s^2.