Two crates of mass m1 = 4.9 kg and m2 = 9.2 kg are connected by a rope that runs

Question

Two crates of mass m1 = 4.9 kg and m2 = 9.2 kg are connected by a rope that runs over a pulley of mass 1.3 kg as shown in the figure below.

http://www.webassign.net/giocp2/8-p-057.gif

(b) Express Newton's second law for the crates (translational motion) and for the pulley (rotational motion). The linear acceleration a of the crates, the angular acceleration ? of the pulley, and the tensions in the right and left portions of the rope are unknowns. (Rpulley is the radius of the pulley, Ipulley is the moment of inertia of the pulley, g is gravitational acceleration, and T1 and T2 are the tensions in the left and right portions of the rope, respectively.)

For the left crate (assume that m1 is moving in the positive direction):

A) ?Fm1 = ?m1g + T1 = m1a

B) ?Fm1 = ?T1 + m2g = m1a

C) ?Fm1 = ?T2 + m2g = m1a

D) ?Fm1 = T2Rpulley ? T1Rpulley = m1a

For the right crate (assume that m2 is moving in the positive direction):

A) ?Fm2 = ?T1 + m2g = m2a

B) ?Fm2 = ?m1g + T1 = m2a


C) ?Fm2 = ?T2 + m2g = m2a

D) ?Fm2 = T2Rpulley ? T1Rpulley = m2a

For the pulley:

A) ?? = T2Rpulley ? T1Rpulley = Ipulley?

B) ?? = ?m1g + T1 = Ipulley?


C) ?? = ?T1 + m2g = Ipulley?

D) ?? = ?T2+m2g = Ipulley?

(c) What is the relation between a and ??

A) a = ?/Rpulley

B) a = Rpulley/?


C) a = 2??Rpulley

D) a = ?Rpulley


(d) Find the acceleration (magnitude only) of the crates.
m/s2

(e) Find the tensions in the right and left portions of the rope.
T1 = N
T2 = N

Explanation / Answer

A) SFm1 = -m1g + T1 = m1a C) SFm2 = -T2 + m2g = m2a A) St = T2Rpulley - T1Rpulley = Ipulleya D) a = aRpulley I = mr^2/2 T2R - T1R = MR^2*a/R T2 -T1 = Ma -m1g + m2g =( m1+m2+m)a (9.2 - 4.9)*9.8 = (9.2+ 4.9 + 1.3) a a = 2.736 m/s^2 T1 = m1a + m1g = 4.9(2.736 + 9.81) = 61.475 N T2 = T1 + ma T2 = 61.475 + 1.3*2.736 T2 = 65.03 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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