A 75 kg astronaut in space pushes against a 200 kg anvil. When the astronaut lets go of the anvil while pushing it:
a. both astronaut and anvil accelerate in opposite directions at the same rate
b. neither the astronaut nor the anvil will accelerate since net force equals zero
c. both accelerate, but the anvil accelerates more than the astronaut.
d. both accelerate, but the anvil accelerates less than the astronaut
To answer this question, we need to understand Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In this case, the action is the astronaut pushing against the anvil. According to Newton's third law, the anvil exerts an equal and opposite force on the astronaut. Therefore, when the astronaut lets go of the anvil, the anvil will also experience a force pushing it in the opposite direction.
Now, let's consider the relationship between force, mass, and acceleration. According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. The equation representing this relationship is:
F = ma
Where F is the force, m is the mass, and a is the acceleration.
Given that the astronaut has a mass of 75 kg and the anvil has a mass of 200 kg, we can conclude that the anvil has a greater mass than the astronaut. In this scenario, since the force applied to both the astronaut and the anvil is the same (due to Newton's third law), the anvil will experience a smaller acceleration compared to the astronaut.
Therefore, the correct answer to the question is: d. both accelerate, but the anvil accelerates less than the astronaut.