Two gliders are set in motion on an air track. A spring of force constant k is a

Question

Two gliders are set in motion on an air track. A spring of force constant k is attached to the back end of the second glider. As shown in the figure below, The first glider, of mass m1, moves to the right with a speed v1, and the second glider, of mass m2, moves more slowly to the right with a speed, v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k. Find the the following.

(a) speed v at maximum compression (Use any variable or symbol stated above as necessary.)

v = ___________________

(b) the maximum compression xmax (Use any variable or symbol stated above as necessary.)

xmax = __________________

(c) the speed of each glider after m1 has lost contact with the spring (Use any variable or symbol stated above as necessary.)

v1f = __________________

v2f = __________________

Two gliders are set in motion on an air track. A spring of force constant k is attached to the back end of the second glider. As shown in the figure below, The first glider, of mass m1, moves to the right with a speed v1, and the second glider, of mass m2, moves more slowly to the right with a speed, v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k. Find the the following. (a) speed v at maximum compression (Use any variable or symbol stated above as necessary.) v = ___________________ (b) the maximum compression xmax (Use any variable or symbol stated above as necessary.) xmax = __________________ (c) the speed of each glider after m1 has lost contact with the spring (Use any variable or symbol stated above as necessary.) v1f = __________________ v2f = __________________

Explanation / Answer

a) conserving momentum,
m1*v1 + m2*v2 = (m1+m2)*v
so, v = (m1*v1+m2*v2)/(m1+m2)

b)conserving energy,
.5*m1*v1^2 + .5*m2*v2^2 = .5*(m1+m2)*v^2 + .5*k*x^2
so, x = sqrt((m1*m2/k)*(v1-v2)^2/(m1+m2))

c) Now use your final speed from part A as your initial speed for this.
Pi=PF
v(m1+m2)= m1v1f + m2v2f

solve for v1f and v2f. I am going to assume you know how to solve this.

Hope this helps

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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