Jane and John, with masses of 54kg and 63kg , respectively, stand on a frictionless surface 11m apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of 0.82m/s2 toward him.


Part A
What is the magnitude of the John's acceleration?

the force is the same on each end of the rope.

forcejohn=forcejane
massjohn*ajohn=massjane*ajane

find ajohn

To find the magnitude of John's acceleration, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

First, let's calculate the force applied to Jane:
Force = mass * acceleration
Force = 54kg * 0.82m/s^2
Force = 44.28N

Since Jane and John are connected by a rope, the force applied to Jane is the same as the force applied by John.

Now, let's calculate the force applied by John:
Force = 44.28N

Next, we can use this force to calculate John's acceleration.
Force = mass * acceleration
44.28N = 63kg * acceleration
Dividing both sides of the equation by 63kg:
acceleration = 44.28N / 63kg
acceleration ≈ 0.7038m/s^2

Therefore, the magnitude of John's acceleration is approximately 0.7038m/s^2.