A hanging mass, M1 = 0.78 kg, is attached by a light string that runs over a frictionless pulley to a mass M2 = 1.48 kg that is initially at rest on a frictionless table. Find the magnitude of the acceleration, a, of M2 in m/s^2.
total mass= M1+M2
force pulling= M1*g
Forcepulling= totalmass*acceleration
To find the magnitude of the acceleration of M2, we can apply 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 = m * a).
In this case, the hanging mass M1 exerts a downward force due to gravity, which is given by the equation F = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The mass M2 experiences an upward tension force in the string, which is due to the hanging mass. Let's assume the acceleration of M2 is a.
Considering the two masses and their acceleration, we can write the following equations:
For M1:
Force due to gravity = m1 * g = 0.78 kg * 9.8 m/s^2
For M2:
Net Force = tension (upward) - force due to gravity (downward) = m2 * a - m2 * g
Since the masses are connected by the same string, the tension in the string is the same for both masses. Therefore, we can equate the tensions:
Tension = m1 * g = m2 * a - m2 * g
Now we can solve for the acceleration, a:
m2 * a - m2 * g = m1 * g
a = (m1 * g + m2 * g) / m2
Substituting the given values:
a = (0.78 kg * 9.8 m/s^2 + 1.48 kg * 9.8 m/s^2) / 1.48 kg
By simplifying the equation, we find:
a ≈ 14.87 m/s^2
Therefore, the magnitude of the acceleration of M2 is approximately 14.87 m/s^2.