1. Two beams have the same cross-sectional area d and length L. Beam A is made o

Question

1. Two beams have the same cross-sectional area d and length L. Beam A is made of material with the density ?A = 3.0 kg/m3 and beam B is made of material with density ?B = 1.0 kg/m3.
a. Which beam has a greater mass?
b. If the two beams are joined end to end with the beam A on the left, where is the center of mass of the new, longer beam of length 2L?
Use the left end of the beam as the origin.
c. For which axis of rotation is the moment of inertia (I) of the beam largest? (a) placed on the left end of the beam; (b) an axis through the center or mass of the beam, perpendicular to its length; (c) an axis placed on the right end of the beam; (d) an axis through the center of the beam along its length.

Explanation / Answer

The relation between the density ant mass , m =V

here m = mass,v = volume and = dencity

(a) If two area's and lengh's are same , the mass depending on the density

m1 = 3dL and m2 = 1dL

hence mass A is grear than the mass of the B.

(b) The center of mass of the system, Xcm = (m1x1+m2x2)/m1+m2

here x1 = L and x2 = 2L+L/2 = 5L/2

Xcm = (3dL*L +1dL*5L/2)/4dL

          = 11L/4

(c) the momentum of inertia of the rod, I = 1/3 ml^2

we substituting m, L values and use Iz = Ix +Iy ,we get the answers.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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