Two small blocks, each of mass m, are connected by a string of constant length 4

Question

Two small blocks, each of mass m, are connected by a string of constant length 4h and negligible mass. Block A is placed on a smooth tabletop as shown above, and block B hangs over the edge of the table. The tabletop is a distance 2h above the floor. Block B is then released from rest at a distance h above the floor at time t=0. Express all algebraic answers in terms of h, m, and g.

A) Determine the acceleration of block B as it descends.

Explanation / Answer

I assume the table is horizontal and no friction. Use FBD of the blocks from t=0 to t= B impacts floor T is the tension in the string Block B m*g-T=m*a Block A T=m*a a) a=g/2 downward b) For Block B y(t)=h-(g*t^2)/4 Block B strikes the floor when y(t1)=0 t1=2*sqrt(h/g) c) Block A has the same acceleration as B until B strikes the floor v(t)=g*t/2 x(t)=g*t^2/4 when x(t1)=h t1=2*sqrt(h/g) d) at t=t1, the speed of block A is v(t1)=g*t1 =2*SQRT(g*h) So for t>t1 before the block falls off the table the velocity is constant and the distance form the edge is 2*h x(t)=2*sqrt(g*h)*t e) when block A leaves the table it has y(t)=2*h-.5*g*t^2 and x(t)=2*sqrt(g*h)*t as long as sqrt(y^2+x^2)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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