A solid cube of wood of side 2a and mass M is resting on a horizontal surface. T

Question

A solid cube of wood of side 2a and mass M is resting on a horizontal surface. The cube is constrained to rotate about an axis AB. A bullet of mass m and speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube. Find the minimum value of v required to tip the cube so that it falls on face ABCD. Assume m M. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) http://www.webassign.net/pse/p11-61.gif

Explanation / Answer

help: mv*4a/3=I(about AB)*w I(about AB)=I(com)+mr*r (r is perpendicular dist. of axis through AB from com r=a{2}^1/2) 4mva/3=[M{4a*a+4a*a}/12+M*{2a}{2a}]*w 4mva/3=8Ma*a*w/3 w=mv/{2Ma} cube will topple if com is at a height of a{2}^1/2 0.5I*w*w=Mga{(2)^1/2-1) 0.5*8Ma*a/3{0.5Mv/{Ma}}^2=Mga{(2)^1/2-1)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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