I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.

I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.

Here are some examples of what kind of problems I want the students to be able to solve with the simulator:

• A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t.
• A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.

I would like the software to have the following features:

• Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.
• Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).
• Show animations of the time evolution of the system.
• Show forces, velocities and accelerations as arrows.
• Give exact numerical results so that the students can use the software to verify their calculation.

Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.

My question is: Is there any software that would meet these requirements and if there is, where could I get it?