The mass of the heavier block is 22 kg and
the mass of the lighter blocks is 11 kg and
the magnitude of the force of the connecting
string on the smaller block is 13 N.
Assume: g = 9.8 m/s
2
and the horizontal
surface on which the objects slide is frictionless.
Determine the force F.
Answer in units of N.
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2.22
To determine the force F, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration (F = ma).
In this case, the force F is the net force acting on the system, and it is responsible for accelerating both the heavier block and the lighter block. Since the blocks are connected by a string, they have the same acceleration.
First, we need to calculate the acceleration of the system. We can use the concept of tension in the string. The tension in the string is the force exerted by the string on the smaller block, which is given as 13 N. This tension is also equal to the force exerted by the smaller block on the string.
Using Newton's second law, we have:
Tension = ma
Substituting the given values:
13 N = (11 kg + 22 kg) * a
Next, we can solve for acceleration (a):
a = 13 N / (11 kg + 22 kg)
a = 13 N / 33 kg
a ≈ 0.394 m/s^2
Now that we have the acceleration, we can determine the force F using Newton's second law:
F = (mass of the lighter block + mass of the heavier block) * acceleration
Substituting the given mass values and the calculated acceleration:
F = (11 kg + 22 kg) * 0.394 m/s^2
F = 33 kg * 0.394 m/s^2
F ≈ 12.99 N
Therefore, the force F is approximately 12.99 N.