The figure shows an Atwood machine (a wheel suspended from the ceiling with two masses connected by a string) with m1 = 1.0 kg and m2 = 1.1 kg. If m2 descends a distance 3m from rest in 3.6 seconds.

1) what is the strength of the gravitational field, g, at this location (N.B. it's not 9.81 N/kg)?

To find the strength of the gravitational field, g, at this location, we can use the information given and apply Newton's second law of motion.

In an Atwood machine, when one mass descends while the other mass ascends, the net force acting on the system is the difference between the gravitational forces on the two masses. This net force is equal to the product of the difference in masses (m1 - m2) and the acceleration of the system.

Using the formula F_net = (m1 - m2) * g, where F_net is the net force, g is the strength of the gravitational field, and m1 and m2 are the masses, we can rearrange the equation to solve for g:

g = F_net / (m1 - m2)

To find the net force, we need the acceleration of the system. We can use the equation of motion to calculate the acceleration:

s = ut + (1/2)at^2

Where s is the distance covered, u is the initial velocity, t is the time taken, and a is the acceleration.

In this case, m2 descends a distance of 3m from rest in 3.6 seconds, so we can substitute the values:

3 = 0 * 3.6 + (1/2) * a * (3.6)^2

Simplifying the equation gives us:

3 = (1/2) * a * (3.6)^2

Solving for a:

a = (2 * 3) / (3.6)^2

a ≈ 0.617 m/s^2

Now we have all the values to calculate the net force:

F_net = (m1 - m2) * a

F_net = (1.0 kg - 1.1 kg) * 0.617 m/s^2

F_net = -0.1 kg * 0.617 m/s^2

F_net ≈ -0.062 kg m/s^2

Since the gravitational force is always positive, we take the magnitude of the net force:

F_net = 0.062 kg m/s^2

Finally, substituting the value of F_net into the equation for g:

g = F_net / (m1 - m2)

g ≈ 0.062 kg m/s^2 / (1.0 kg - 1.1 kg)

g ≈ 0.062 kg m/s^2 / -0.1 kg

g ≈ -0.62 N/kg

Therefore, the strength of the gravitational field at this location is approximately -0.62 N/kg.