A 10kg mass and a 2.0kg mass are connected by a light string over a massless, frictionless pulley. if g=9.8ms^-2, what is the acceleration of the system when released? (98ms^-2)
To determine the acceleration of the system, we need to analyze the forces acting on each mass.
Let's denote the 10kg mass as m1 and the 2.0kg mass as m2. The force due to gravity acting on m1 is given by F1 = m1 * g, where g is the acceleration due to gravity.
In the case of m2, the force due to gravity is given by F2 = m2 * g.
When the system is released, the 10kg mass will experience a downward force of F1 due to gravity, while the 2.0kg mass will experience an upward force of F2 due to gravity. As the string connecting them is light, we can assume that the tension in the string is the same on both sides of the pulley.
The net force acting on m1 is the difference between the force due to gravity and the tension in the string, which is given by:
Net force on m1 = F1 - T
The net force acting on m2 is the sum of the force due to gravity and the tension in the string, which is given by:
Net force on m2 = T - F2
According to Newton's second law of motion, the net force on an object is equal to the mass of the object multiplied by its acceleration. Therefore, we can write the following equations for the acceleration of m1 and m2:
m1 * a = F1 - T
m2 * a = T - F2
Since we have two equations and two unknowns (T and a), we can solve for the acceleration (a) using these equations.
Substituting the values, we get:
10kg * a = (10kg * 9.8m/s^2) - T
2.0kg * a = T - (2.0kg * 9.8m/s^2)
Now, we can eliminate T by adding the two equations:
10kg * a + 2.0kg * a = (10kg * 9.8m/s^2) - (2.0kg * 9.8m/s^2)
12kg * a = 98kg * m/s^2
Dividing both sides by 12kg, we find:
a = (98kg * m/s^2) / 12kg
a ≈ 8.17m/s^2
Therefore, the acceleration of the system when released is approximately 8.17m/s^2.