Two blocks are arranged at the ends of a massless
string as shown in the figure. The system
starts from rest. When the 4.01 kg mass has
fallen through 0.412 m, its downward speed is
1.3 m/s.
The acceleration of gravity is 9.8 m/s
2
.
Incomplete.
To find the tension in the string and the mass of the second block, we can use the principles of Newtonian mechanics.
First, let's consider the 4.01 kg mass. We know its downward speed and the distance it has fallen. We can use the following kinematic equation to relate these quantities:
v^2 = u^2 + 2as
where v is the final speed (1.3 m/s), u is the initial speed (0 m/s since it starts from rest), a is the acceleration (acceleration due to gravity, -9.8 m/s^2 since it is acting in the opposite direction of motion), and s is the distance fallen (0.412 m).
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Substituting the given values, we get:
a = (1.3^2 - 0^2) / (2 * 0.412)
a = 2.758 m/s^2
Now, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = ma
In this case, the net force is the tension in the string, and the mass is 4.01 kg. Rearranging the equation, we get:
T = ma
T = 4.01 * 2.758
T = 11.049 N
So, the tension in the string is 11.049 N.
To find the mass of the second block, we can use the fact that the tension in the string is the same throughout. The second block experiences the same tension as the first block. Let's assume the mass of the second block is m.
Using Newton's second law again, we can establish the following equation:
T = (m + 4.01) * 9.8
Substituting the value of the tension calculated (11.049 N), we get:
11.049 = (m + 4.01) * 9.8
Simplifying and solving for m:
11.049 / 9.8 = m + 4.01
1.129 = m + 4.01
m = 1.129 - 4.01
m = -2.881 kg
Since the mass cannot be negative, it implies there must be an error in the calculation or the assumptions made. Please double-check the given values and equations used.