Nonuniform cylindrical object. In the figure below, a cylindrical object of mass

Question

Nonuniform cylindrical object. In the figure below, a cylindrical object of mass M and radius R rolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.503 m from the end of the ramp. The initial height of the cylinder is H = 0.990 m; the end of the ramp is at height h = 0.10 m. The object consists of an outer cylindrical shell (of a certain uniform density) that is glued to a central cylinder (of a different uniform density). The rotational inertia of the object can be expressed in the general form I-BMR2, but B is not 0.5 as for a cylinder with a single uniform density. Determine B. 1.43

Explanation / Answer

it will leave ramp horizontally,

after that in vertical direction, v0y = 0

ay = - 9.81 m/s^2

y = 0 - h = 0.10 m

y = v0y t + ay t^2 /2

- 0.10 = 0 - 9.81 t^2 /2

t= 0.143 sec

in horizontal, v = d/ t = 3.523 m/s

Now applying energy conservation from H to h.

m g H + 0 = m g h + m v^2 /2 + I w^2 /2

m g (H - h) = m v^2 /2 + (beta m r^2) (v / r)^2 / 2

g (H - h) = v^2 /2 + beta v^2 / 2

2 x 9.81 x (0.990 - 0.10) = v^2 (1 + beta)

1 + beta = 1.41

beta = 0.41 .........Ans

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

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