As shown below, three blocks are connected by a cord which passes over two frict

Question

As shown below, three blocks are connected by a cord which passes over two frictionless, massless pulleys. Two of the blocks are hanging, while the third is on a frictionless horizontal surface. A spring of constant = 317 N/m is attached to the block of mass m_1 The masses of the blocks are: m_1 = 217 kg, m_2 = 390 kg, and m_3 = 50kg. The system is released from rest with the spring initially neither compressed nor stretched. Please find the speed v of block 2 when it has fallen a distance h = 2.83 m. Note that U_s = mgh, U_1 = 1/2 kx^2, and K = 1/2 mv^2.

Explanation / Answer

Here ,

k = 317 N/m

m1 = 217 Kg

m2 = 390 Kg

m3 = 50 Kg

let the speed of block 2 is v

Using conservation of energy

0.5 * m1 * v^2 + 0.5 * m2 * v^2 + 0.5 * m3 * v^2 + 0.5 * k * h^2 = m1 * g * h - m2 * g * h

as h = 2.83 m

0.5 * 217 * v^2 + 0.5 * 390 * v^2 + 0.5 * 50 * v^2 + 0.5 * 317 * 2.83^2 = (390 - 217) * 9.8 * 2.83

solving for v

v = 3.28 m/s

the speed of block 2 after falling a distance h = 2.83 m is 3.28 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.