A crate of mass m1 on a frictionless inclined plane is attached to another crate

Question

A crate of mass m1 on a frictionless inclined plane is attached to another crate of mass m2 by a massless rope. The rope passes over an ideal pulley so the mass m2 is suspended in air. The plane is inclined at an angle theta=16.7 degrees. Use conservation of energy to find how fast crate m2 is moving after m1 has traveled a distance of 1.8 m along the incline, starting from rest. The mass of m1 is 10.1 kg and the mass of m2 is 12.1 kg.

Explanation / Answer

from using the conservation of energy principle ==>total energy at initial state =total energy at final state total energy at initial state=potential energy at initial state+kinetic energy at initial state ==>potential energy at initial state= 0 (take this position as the reference) ==>kinetic energy at initial state=0 (both masses are at rest initially) similarly potential energy at final state=-m2*g*1.8+m1*g*1.8*sina (a=inclination angle) kinetic energy at final state=0.5(m1v1^2 +m2v1^2) (v1=velocity of both masses(both have same velocities because if they have different velocities then the rope connecting would go slack or extend in length which is impossible )) ==>from using the conservation of energy principle 0=-m2*g*1.8+m1*g*1.8*sina+0.5(m1v1^2 +m2v1^2) ==>12.1*g*1.8 - 10.1*g*1.8sin16.7=0.5(m1v1^2 +m2v1^2) ==>185.00=0.5(m1v1^2 +m2v1^2) ==>v1=(185*2/(m1+m2))^0.5 ==>v1=4.08 m/s velocity of crate m2=4.08 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.