cart A with mass: 512g (0.512kg) is on a horizontal table. the cart is connected to cart b with mass: 51.0g (0.051kg) through a string that is crossing a pulley. cart A is released from rest at 60 cm(0.60m), it passes a photogate with a velocity of 0.90m/s. What is the work done by the non conservative force?

To find the work done by the non-conservative force on the cart, we can use the work-energy principle.

The work done by a force is given by the formula:

Work = Force x Displacement x cos(θ)

In this case, the non-conservative force is acting on cart A as it moves, so we need to find the force acting on cart A.

To find the force, we can use Newton's second law:

Force = Mass x Acceleration

In this case, the acceleration can be calculated using the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity of cart A (0.90 m/s)
u = initial velocity of cart A (0 m/s, since the cart is released from rest)
a = acceleration of cart A
s = displacement of cart A (0.60 m)

Rearranging the equation, we have:

a = (v^2 - u^2) / 2s

Let's calculate the acceleration:

a = (0.90^2 - 0^2) / (2 * 0.60)
a = 0.405 m/s^2

Now we can calculate the force:

Force = Mass x Acceleration
Force = 0.512 kg x 0.405 m/s^2
Force = 0.20736 N

Now that we have the force and the displacement (0.60 m), we can calculate the work done by the non-conservative force:

Work = Force x Displacement x cos(θ)

Since the force and displacement are in the same direction (horizontal), the angle between them is 0 degrees:

θ = 0 degrees

cos(0) = 1

Work = 0.20736 N x 0.60 m x 1
Work = 0.124416 J

Therefore, the work done by the non-conservative force on the cart is 0.124416 Joules.