A 5.8 kg mass, M1 is on a horizontal frictionless table. A horizontal string is attached to M1 and it passes over a pulley at the edge of the table to a 5.6kg mass M2 that is hanging down freely. Initially the two masses are held stationary and then released. Calculate the magnitude of the acceleration of the masses
f = m a
the force is the weight of the hanging mass
the mass is the sum of the two masses
To calculate the magnitude of the acceleration of the masses, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration.
For mass M1 on the table, the only force acting on it is the tension in the string. Since the table is frictionless, there is no frictional force to consider.
For mass M2 hanging freely, the only force acting on it is the force due to its weight, which is given by the equation F = m * g, where m is the mass of M2 and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the two masses are connected by the string, which passes over a pulley, the tension in the string will be the same for both masses. Let's denote this tension force as T.
Now, using Newton's second law for each mass, we can set up the following equations:
For M1:
T = M1 * a
For M2:
m2 * g = T - M2 * a
Since both masses have the same acceleration (a), we can solve these two equations simultaneously to find the unknown acceleration.
Substituting the expression for T from the first equation into the second equation, we get:
M1 * a = M2 * g + M2 * a
Rearranging the equation, we can isolate the acceleration:
a * (M1 + M2) = M2 * g
Finally, dividing both sides of the equation by (M1 + M2), we obtain the magnitude of the acceleration:
a = (M2 * g) / (M1 + M2)
Now you can substitute the given values for M1 (5.8 kg) and M2 (5.6 kg) into this equation, along with the value for g, to calculate the magnitude of the acceleration.