2-body problems-Need help calculating

[ohmygenevieve]

2-body problems--Need help calculating!

A 20 kg block (A) rests on a frictionless table; a cord attached to the block extends horizontally to a pulley at the edge of the table. A 10 kg mass (B) hangs at the end of the cord.
a) Clearly draw and label the force vectors acting on each object.
b) Calculate the acceleration of the block and mass.
c) Calculate the tension in the cord.
I do not understand how to calculate the Net force. I do know that I need the Net force to get the acceleration of the block and mass, because F_Net= m * a.
Also, I need help on calculating the tension in the cord as well. I don't know which numbers to use or how to get numbers for the equation if they aren't a given...
Thanks so much!
-Genevieve

 

[technician]

Your starting point is to realize that the tension, T, in the connecting cord exerts a horizontal force,T, on the 20kg block and a vertical (up) force of T on the 10kg mass.
Draw this diagram and apply F=ma to each object. (simultaneous equations !)

 

[technician]

Or... you could realize that there is only 1 external force... due to the WEIGHT of the hanging 10kg block, and this force accelerates all of the mass of the blocks. This will give you the acceleration straight away but you will then need to calculate the tension in the connecting string.

 

[ehild]

Genevieve, the first thing to do is to draw a picture, and "Clearly draw and label the force vectors acting on each object."

Show that drawing, please.

ehild

 

[asteriatic]

I would be happy to help you with your 2-body problem calculations. First, let's start with drawing and labeling the force vectors for each object. For the 20 kg block (A), we have the force of gravity (mg) acting downwards and the normal force (N) acting upwards since the block is resting on a frictionless surface. For the 10 kg mass (B), we have the force of gravity (mg) acting downwards and the tension force (T) acting upwards since it is hanging from the cord.

To calculate the acceleration of the block and mass, we can use Newton's second law, F=ma. Since there are no external forces acting on the system, the net force (FNet) is equal to the sum of all the individual forces. So for the block, we have FNet = N - mg and for the mass, we have FNet = T - mg. Since we know the masses of each object, we can plug these values into the equation and solve for acceleration (a).

To calculate the tension in the cord, we can use the same equation, F=ma, but this time we will use the acceleration we just calculated. The tension force (T) is equal to the mass of the hanging object (10 kg) multiplied by the acceleration we just found.

I hope this helps you with your calculations. Remember to always draw and label your force vectors and use Newton's laws of motion to solve for unknown quantities. Good luck!