A m1 = 4.20-kg block on a smooth tabletop is attached by a string to a hanging block of mass m2 = 2.60 kg, as shown in the figure. The blocks are released from rest and allowed to move freely.
To determine the acceleration of the system and the tension in the string connecting the two blocks, we need to analyze the forces acting on the blocks.
First, let's consider the forces acting on the hanging block (m2). The only force acting on it is its weight (m2 * g), where g is the acceleration due to gravity (9.8 m/s^2).
Next, we analyze the forces acting on the block on the tabletop (m1). There are two forces acting on it: the tension force (T) in the string and the weight of the block (m1 * g).
Since the blocks are connected by the string, they undergo the same acceleration, denoted as 'a'. According to Newton's second law, the sum of the forces acting on each block in the direction of motion is equal to the mass of the block times its acceleration.
For the hanging block (m2):
m2 * g - T = m2 * a (Equation 1)
For the block on the tabletop (m1):
T - m1 * g = m1 * a (Equation 2)
We now have a system of two equations with two unknowns (T and a). We can solve this system to find the values of tension (T) and acceleration (a).
To do that, we can add Equation 1 and Equation 2 together:
m2 * g - T + T - m1 * g = m2 * a + m1 * a
Simplifying the equation, we have:
m2 * g - m1 * g = (m2 + m1) * a
Now, we can calculate the acceleration (a):
a = (m2 * g - m1 * g) / (m2 + m1)
With the given masses (m1 = 4.20 kg and m2 = 2.60 kg) and acceleration due to gravity (9.8 m/s^2), we can substitute these values into the equation to find the acceleration (a).
Finally, once we have the value of acceleration (a), we can substitute it back into either Equation 1 or Equation 2 to solve for the tension (T).