A 160 kg astronaut (including space suit) acquires a speed of 2.20 m/s by pushing off with his legs from an 1950 kg space capsule.
What is the change in speed of the space capsule? As the reference frame, use the position of the space capsule before the push.
If the push lasts 0.47 s, what is the average force exerted on the astronaut by the space capsule?
To find the change in speed of the space capsule, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the push is equal to the total momentum after the push.
The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum before the push is given by:
Initial momentum = mass of the astronaut × initial speed of the astronaut + mass of the space capsule × initial speed of the space capsule
The momentum after the push is given by:
Final momentum = mass of the astronaut × final speed of the astronaut + mass of the space capsule × final speed of the space capsule
Since we are using the position of the space capsule as the reference frame, the initial speed of the space capsule is zero.
Initial momentum = (mass of the astronaut × initial speed of the astronaut) + (mass of the space capsule × 0)
Final momentum = (mass of the astronaut × final speed of the astronaut) + (mass of the space capsule × final speed of the space capsule)
Momentum before the push = Momentum after the push
(mass of the astronaut × initial speed of the astronaut) = (mass of the astronaut × final speed of the astronaut) + (mass of the space capsule × final speed of the space capsule)
Substituting the given values:
(160 kg × 2.20 m/s) = (160 kg × final speed of the astronaut) + (1950 kg × final speed of the space capsule)
Now, we can solve this equation to find the final speed of the space capsule.
To find the average force exerted on the astronaut by the space capsule, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
Force = (change in momentum) / (time)
The change in momentum is given by:
Change in momentum = Final momentum - Initial momentum
Substituting the given values, we can find the change in momentum.
Then, we can calculate the average force exerted on the astronaut by dividing the change in momentum by the given time of 0.47 s.