A block of mass m1 = 3.56 kg on a frictionless plane inclined at angle θ = 34.1° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.72 kg hanging vertically (see the figure). (a) What is the acceleration of the hanging block (choose the positive direction down)? (b) What is the tension in the cord?
No drawing so I can't see the angle but..
m1gcos34.1 - m2g = (m1+m2)a
solve for a
T - m2g = m2a
If this doesn't work out use sin34.1 instead. One of the two will work.
To find the acceleration of the hanging block and the tension in the cord, we can follow these steps:
(a) Find the net force acting on the system:
The force acting on the hanging block is its weight, given by F2 = m2 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
The force acting on the inclined block is the component of its weight along the inclined plane, which is F1_parallel = m1 * g * sin(θ).
(b) Calculate the acceleration:
Since the blocks are connected and will move together, the tension in the cord will be the same for both blocks.
Using Newton's second law, which states that the net force (F_net) on an object is equal to its mass (m) multiplied by its acceleration (a), we can set up an equation for the system:
F_net = F2 - F1_parallel = (m2 * g) - (m1 * g * sin(θ))
The tension in the cord can be expressed as:
T = m2 * a
Now we have two equations:
1. F_net = (m2 * g) - (m1 * g * sin(θ))
2. T = m2 * a
Solving these two equations simultaneously will help us find the acceleration (a) and the tension in the cord (T).