Two masses, m1 and m2, are connected to each other as the figure below shows. Mass m1 slides on a frictionless surface over the table. Both masses have acceleration of magnitude as shown. How does the tension in the string compare to the weight, m2g, of m2?
We can start by applying Newton's second law to each mass separately. For m1, we have:
m1a = T
where T is the tension in the string. For m2, we have:
m2a = m2g - T
where m2g is the weight of m2.
We can use the given information about the accelerations to write:
a = 2m/s^2
and
a = 3m/s^2
for m1 and m2, respectively.
We can now use algebra to solve for T. From the first equation, we have:
T = m1a
Substituting this into the second equation, we get:
m2a = m2g - m1a
Solving for m2g, we get:
m2g = m2a + m1a
Substituting the given values for m1, m2, and a, we get:
m2g = (2kg)(3m/s^2) + (1kg)(2m/s^2) = 8N
Therefore, the weight of m2 is 8N.
To find the tension in the string, we can substitute this value of m2g into one of the earlier equations. Using the equation for m1, we get:
T = m1a = (1kg)(2m/s^2) = 2N
Therefore, the tension in the string is 2N, which is less than the weight of m2.