A mass, m1 = 5.00 kg, resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 9.0 kg. Find the acceleration of each mass and the tension in the cable.
PLEASE HELP!
To solve this problem, we can use Newton's second law of motion.
First, let's find the acceleration of the system. We will consider the two masses separately.
For mass m1, the only force acting on it is the tension in the cable. Using Newton's second law, we have:
m1 * a = T
where a is the acceleration of mass m1 and T is the tension in the cable.
For mass m2, the force acting on it is the gravitational force pulling it downwards, which is given by:
m2 * g
where g is the acceleration due to gravity.
The tension in the cable is the force that accelerates mass m2 upwards, so we have:
T - m2 * g = m2 * a
Now, we can solve these two equations to find the acceleration (a) and the tension (T).
From the first equation, we can write:
a = T / m1
Substituting this into the second equation, we have:
T - m2 * g = m2 * (T / m1)
Now, we can solve for T:
T - m2 * g = (m2 / m1) * T
T - (m2 / m1) * T = m2 * g
T * (1 - m2 / m1) = m2 * g
T = (m2 * g) / (1 - m2 / m1)
Substituting the given values of m1 = 5.00 kg and m2 = 9.0 kg, and taking g as approximately 9.8 m/s^2, we can calculate the tension:
T = (9.0 kg * 9.8 m/s^2) / [1 - (9.0 kg / 5.00 kg)]
Once we have calculated the tension, we can substitute it back into the first equation to find the acceleration of mass m1:
a = T / m1
Finally, we have the acceleration of both masses and the tension in the cable.