3. Box, mass m1, at rest against a compressed spring, spring constant k and comp

Question

3. Box, mass m1, at rest against a compressed spring, spring constant k and compression of Delta x, at the top of a ramp, height h,is released. It slides down the ramp, angle theta, with friction, coefficient Mu. Half way down the ramp. it bumps into and sticks to another box, mass m2, and together, they slide to the bottom. If m1 = 2.0 kg. m2= 3.0 kg, k = 500 N/m, delta x = 0.40 m, h = 5.0 m, mu = 0.30, theta = 30.0 degree, how long does it take both boxes to reach the bottom (starting from when the first box separates from the spring)? The spring is parallel to the ramp surface and the deltax is measured parallel to the ramp surface.

Explanation / Answer

at starting .

spring's P.E> = K.E. of mass

kx^2 /2 = mu^2 /2

u = x.sqrt(k/m) =0.40 x sqrt(500 / 2) = 6.32 m/s

now perpendicular to ramp ;

N = mgcos@   = 2gcos30

along the ramp :

mgsin@ - f = ma

2gsin30 - 0.30*2gcos30 =2a

a = 2.36 m/s2

L = h/sin30 = 10m

at halfway down d = L/2 = 5 m

using v^2 - u^2   = 2ad

v^2 - 6.32^2 = 2 x 2.36 x 5

v = 7.97 m/s

t1 = v - u / a   = 7.97 - 6.32 / 2.36 = 0.70 sec

after that they go together

now using momentum conservation,

initial = final momentum,

2 x 7.97 + 0 = (2 +3)vf

vf =3.19 m/s

now using h = ut + at^2 /2

-5 = -3.19t - 2.36t^2 /2

1.18t^2 + 3.19t - 5 =0

on solving

t = 1.10 sec

total time = 0.70 +1.10 = 1.80 sec

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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