How Do You Calculate Acceleration and Tension in a Frictionless System?

[Aherald117]

Question Details:
a 21 kg block sliding on a 13 kg block. All surfaces are frictionless. Find the magnitude of acceleration of each block and the tension in the string that connects the blocks.
Find the acceleration m/s2 (acceleration of blocks)?
and the force N (tension in string) ?

Have found Efy to be 301.5 and Efx to be -82.01, i set the Efy equal to 0 but i don't know if I am suppose to add the Efy to the Efx before I set that information equal to M*a to get the acceleration

 

[PhanthomJay]

A picture would help. Or more details with the question, it is not complete.

 

[m2003]

.

I would first like to commend you on your efforts in solving this problem. It seems like you have a good understanding of the concept of energy and its conservation in this situation.

To answer your question, yes, you are correct in setting the net force in the y-direction (Efy) equal to 0. This is because there is no friction involved, so there is no force acting in the y-direction. Therefore, the net force in the y-direction should be equal to 0 according to Newton's first law.

However, in the x-direction, there is a net force acting on the blocks due to the difference in their masses. This is where we can use the equation Efx = M*a to find the acceleration of the blocks. Since you have already calculated Efx to be -82.01, you can simply divide this value by the total mass of the system (21 kg + 13 kg = 34 kg) to find the acceleration of the blocks, which should be approximately -2.41 m/s^2.

As for the tension in the string, we can use the equation F = M*a to find this value. Since we now know the acceleration of the blocks, we can plug this value in along with the mass of the smaller block (13 kg) to find the tension in the string, which should be approximately 31.33 N.

I hope this helps clarify your doubts and assists you in solving the problem. Keep up the good work!