How Do You Calculate Acceleration in a Two-Mass System with Newton's Laws?

[dorkee]

Homework Statement

A 10.0-kg mass on a frictionless table is accelerated by a 5.0-kg mass hanging from a table. Calculate the acceleration of the mass on the table. (It gives a picture but I can draw it if nobody can picture the diagram).

Homework Equations

F=ma
F=mg

The Attempt at a Solution

Okay, so I don't even know if I'm going in the right direction but I did this so far:
I solved for the force for the 5.0 kg block which is the one hanging from the table.
F=ma
F = (5.0 kg)(9.8 m/s^2)
F = 49 N

And now I'm just stuck.

 

[Kurdt]

Draw a free body diagram of each block and find the net forces acting on them.

 

[baba89]

I would approach this problem by first identifying the relevant forces acting on the 10.0-kg mass on the frictionless table. From the given information, we know that the force of gravity (weight) acting on the 5.0-kg mass is 49 N, as you correctly calculated.

Next, we need to consider the force of tension in the string connecting the two masses. Since the string is assumed to be massless and the table is frictionless, the tension in the string must be the same at both ends. Therefore, the 10.0-kg mass experiences a tension force of 49 N as well.

Now, we can apply Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force acting on the 10.0-kg mass is the tension force of 49 N, and its mass is 10.0 kg. Therefore, we can solve for the acceleration using the equation F=ma:

49 N = (10.0 kg)(a)
a = 4.9 m/s^2

So, the acceleration of the 10.0-kg mass on the frictionless table is 4.9 m/s^2. This means that the mass will accelerate at a rate of 4.9 meters per second squared in the direction of the tension force.

It is important to note that this solution assumes ideal conditions, such as a perfectly frictionless table and massless string. In reality, there may be slight variations due to external factors, but the overall concept of Newton's Law of Acceleration still applies.