You are enjoying the frictionless frozen surface of the Rideau canal with your friend. While together, you try a physics experiment in which you push off of each other at the same time. If your acceleration is 2 m/s 2, what is your friend’s acceleration, in m/s 2, if your mass is 64.2 kg and your friend’s is 58.8 kg?
To solve this problem, we need to apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, when you push off your friend, you exert a force on your friend, and your friend exerts an equal and opposite force on you.
First, let's calculate the force you exert. We can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).
Given:
Mass (yours): 64.2 kg
Acceleration (yours): 2 m/s^2
Plugging in the values, we can calculate the force you exert on your friend:
Force (yours) = 64.2 kg * 2 m/s^2 = 128.4 N
Since the forces exerted are equal and opposite, the force your friend exerts on you is also 128.4 N.
Now let's calculate your friend's acceleration using Newton's second law of motion. We rearrange the formula to solve for acceleration (a = F / m).
Given:
Force (friend's) = 128.4 N
Mass (friend's) = 58.8 kg
Plugging in the values, we can calculate your friend's acceleration:
Acceleration (friend's) = 128.4 N / 58.8 kg ≈ 2.18 m/s^2
Therefore, your friend's acceleration is approximately 2.18 m/s^2.