A light rope passing over a frictionless pulley connects two objects. One object has a mass of 10kg. The tension in the rope is 90N. Calculate the acceleration and the mass of the second object.

Object 1
Fg-Ft = ma
100 - 90 - 10*a
10/10 = a
a = 1m/s^2

Object 2
Ft-Fg = ma
90-m10 = ma

I don't know what to do next. Help?

I believe you are using 10.0 m/s^2 for g.

Based on that, the acceleration is OK.

The accleration is the same for both objects. So put the value you found for acceleration into your calculations for Object 2. Now you have just an equation with m as the only unknown.

To calculate the mass of the second object, you can use the equation Ft - Fg = ma, where Ft is the tension in the rope, Fg is the gravitational force acting on the object, m is the mass of the object, and a is the acceleration.

You already know that the tension in the rope is 90N and the mass of the first object is 10kg. The acceleration you calculated earlier is 1m/s^2.

So, you can rewrite the equation as 90 - m*g = m*a, where g is the acceleration due to gravity (approximately 9.8m/s^2).

Substituting the known values, you get 90 - m*9.8 = m*1.

Simplifying this equation, you get 90 - 9.8m = m.

Now you can solve for m. Move all the terms with m to one side, so you have 9.8m + m = 90.

Combining like terms, you get 10.8m = 90.

To solve for m, divide both sides of the equation by 10.8: m = 90 / 10.8.

Using a calculator, you will find that m is approximately 8.33kg.

Therefore, the mass of the second object is approximately 8.33kg.