A large spring is used to stop the cars after they come downthe last hill of a r

Question

A large spring is used to stop the cars after they come downthe last hill of a roller coaster. The cars start at rest at thetop of the hill and are caught by a mechanism at the instant theirvelocities at the bottom are zero. Compare the compression of thespring, xA, for a fully loaded car with that,xB, for a lightly loaded car whenmA = 2mB.
xA = xB.
xA =xB.
xA = xB.
xA = 2xB.
xA = 4xB.

Explanation / Answer

A large spring isused to stop the cars after they come down the last hill of aroller coaster. The cars start at rest at the top of the hill andare caught by a mechanism at the instant their velocities at thebottom are zero. Compare the compression of the spring,xA, for a fully loaded car with that,xB, for a lightly loaded car whenmA =2mB. {K.E. Of Car A@ Spring} = {Init P.E. Of Car A} = (2*M)*g*h ---->    {Final Spring P.E.For Car A} = {K.E. Of Car A @Spring} ---->   (1/2)*k*(x_A)^2 = (2*M)*g*h ---->    (x_A) = {4*M*g*h/k} {K.E. Of Car B @ Spring} = {Init P.E. Of CarB} = (M)*g*h ---->    {Final Spring P.E.For Car B} = {K.E. Of Car B @Spring} ---->   (1/2)*k*(x_B)^2 = (M)*g*h ---->    (x_B) = {2*M*g*h/k} ---->    (x_A)/(x_B) = {4*M*g*h/k}/{2*M*g*h/k} = 2 ---->    (x_A) = (2)*(x_B) .

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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