The three air carts have masses , reading from left to right,of m, 2m, and 4m, r

Question

The three air carts have masses , reading from left to right,of m, 2m, and 4m, respectively. Initially, the cart on theright (4m) is at rest, whereas the other two carts are moving tothe right with a speed V0. All carts are equippedwith putty bumpers that give completey inelasticcollisions. Find the final speed of the carts. Calculate the ratio of the final kinetic energy of the systemto the initial kinetic energy. The three air carts have masses , reading from left to right,of m, 2m, and 4m, respectively. Initially, the cart on theright (4m) is at rest, whereas the other two carts are moving tothe right with a speed V0. All carts are equippedwith putty bumpers that give completey inelasticcollisions. Find the final speed of the carts. Calculate the ratio of the final kinetic energy of the systemto the initial kinetic energy.

Explanation / Answer

masses m = m            m' = 2 m           m"= 4m Initial velocities u = vo                     u ' = vo                     u " = 0     Since it is at rest from law of conservation momentum , mu + m' u' + m" u "= ( m+ m' + m" ) v from this final speed of carts v = [ mu + m' u ' + m" u" ] / ( m + m' + m " )                                                = 3mvo / ( 7 m)                                                = 0.4285 vo (b). final kinetic energy K ' = ( 1/ 2) ( m+ m' + m" ) v^ 2                                          = 0.6428 m vo^ 2 initila kinetic energy K = ( 1/ 2) mu ^ 2 + ( 1/ 2) m' u' ^ 2+ ( 1/ 2) m " u" ^ 2                                   = ( 1/ 2) mvo^ 2 + mvo^ 2 + 0                                   = 1.5 mvo^ 2 required ratio = K ' / K = 0.4285

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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