A 8.7 kg block is on a frictionless surface. It is connected by a string over a pulley to a 8.6 kg hanging mass. Find the acceleration of the block.
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To find the acceleration of the block, we need to apply Newton's second law of motion. This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this situation, there are two forces at play: the force due to the weight of the hanging mass (m1) and the force caused by the tension in the string (T). The force due to gravity acting on the hanging mass is given by the equation:
F1 = m1 * g
The tension in the string is the same for both masses and can be calculated using the equation:
T = m2 * a
where m2 is the mass of the block and a is its acceleration.
Since the block is on a frictionless surface, there is no additional force acting on it. Therefore, we can write the following equation using Newton's second law:
F1 - T = m2 * a
Substituting the expressions for F1 and T into the equation, we have:
m1 * g - m2 * a = m2 * a
Simplifying the equation, we get:
m1 * g = 2 * m2 * a
Now, we can solve for the acceleration (a):
a = (m1 * g) / (2 * m2)
Substituting the given values, we have:
a = (8.6 kg * 9.8 m/s^2) / (2 * 8.7 kg)
Upon calculation, the acceleration of the block is approximately 4.743 m/s^2.