Question

The string connecting the m1 and the m2 passes over a light frictionless pulley. Given m1 = 3.37 kg, m2 = 5.46 kg, m3 = 6.13 kg, and g = 9.8 m/s 2 . The acceleration of gravity is 9.8 m/s 2 . Find the downward acceleration of m2 mass. Answer in units of m/s 2 .

Answer 1

(The image of the problem is attached below)

Answer:

$440.29\frac{m}{s^{2}}$

Explanation:

Analyzing forces on m2 we can se that there are three forces on it. F1 that is the force the m1 mass does on 2, F3 that is the force the m3 mass does on 2 and finally the weight W of block two. If we choose downwards as positive direction the net force is:

$F= F_3+W_2-F_1$

because Newton's third law the force F3 the chord does to m2 is equal to the weight of 3 and the same for 1, so (1) is:

$F=W_3+W_2-W_1=m_3g+m_2g-m_1g=g(m_3+m_2-m1)$

$F=(9.81)(6.13+5.46-3.37)=80.64 N$

Now we can find the acceleration (a) using Newton's second law:

$F=m_2a$

Solving for a:

$a=\frac{F}{m_2}=\frac{80.64}{5.46}=440.29\frac{m}{s^{2}}$