A student goes to planet x and wants to determine the gravity there. The student knows from physics lab that they can use Atwood's machine to determine gravity. The student places a 100g mass and a 110g mass at the end of a string and hangs it over a pulley. The student places the 110g mass one meter above the ground and times its fall as being 0.3 seconds. What is gravity on planet x?

average velocity= (1/.3) m/s

final velocity= 2*avg velocity= 2/.3

final KE= change in PE
1/2 * (.100+.110)(2/.3)^2=(.110-.100)"g"

solve for "g"

To determine the gravity on planet X using Atwood's machine, we can start by understanding the basic concept behind Atwood's machine.

Atwood's machine is a setup consisting of two masses connected by a string or a cable passing over a pulley. The difference in the masses causes a net force, which leads to acceleration and allows us to calculate the gravity.

In this scenario, we have a 100g mass and a 110g mass. The 100g mass will be moving upwards while the 110g mass falls due to the force of gravity.

First, let's calculate the net force acting on the masses:

Net force = (mass2 * gravity) - (mass1 * gravity)

Where:
mass1 is the 100g mass
mass2 is the 110g mass
gravity is the unknown gravity on planet X.

Next, we need to calculate the acceleration of the masses. We assume that the string and the pulley have negligible mass and friction:

Acceleration = Net force / Total mass

Where:
Total mass = mass1 + mass2

Finally, we can calculate the gravity using the acceleration and the time it takes for the 110g mass to fall, as follows:

Gravity = 2 * Distance / (Time^2)

Where:
Distance is the height of the 110g mass (1 meter in this case)
Time is the time it takes for the 110g mass to fall (0.3 seconds in this case)

By plugging in the given values, we can calculate the gravity on planet X as follows:

Net force = (110g * gravity) - (100g * gravity)
Total mass = 100g + 110g
Acceleration = Net force / Total mass
Gravity = 2 * 1 meter / (0.3 seconds)^2

Calculating these values will give you the gravity on planet X.

To determine the gravity on planet X using Atwood's machine, we can use the formula:

g = (m2 - m1) * (2π / T)²

Where:
g = gravity on planet X
m1 = mass 1 (100g)
m2 = mass 2 (110g)
T = time taken for mass 2 to fall (0.3 seconds)

First, convert the masses from grams to kilograms:
m1 = 100g = 0.1kg
m2 = 110g = 0.11kg

Next, substitute the values into the formula and solve for g:
g = (0.11kg - 0.1kg) * (2π / 0.3s)²

Now, calculate the expression within the parentheses:
g = 0.01kg * (2π / 0.3s)²

To solve this equation further, we need to use the value of π, which is approximately 3.14. We also need to square the fraction (2π / 0.3s)²:

g = 0.01kg * (2 * 3.14 / 0.3s)²

g = 0.01kg * (6.28 / 0.3s)²

Now, calculate the square of the fraction:
g = 0.01kg * (20.93s²)
g = 0.2093 kg * s²

Therefore, the gravity on planet X, as determined by the Atwood's machine, is approximately 0.2093 kg*m/s².