Three blocks are connected on the table as shown below. The coefficient of kinet

Question

Three blocks are connected on the table as shown below. The coefficient of kinetic friction between the block of mass m2 and the table is 0.380. The objects have masses of m1 = 3.75 kg, m2 = 1.50 kg, and m3 = 2.40 kg, and the pulleys are frictionless.

(b) Determine the acceleration of each object, including its direction.

(c) Determine the tensions in the two cords.

(d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same?

Explain.

m1: magnitude m/s2
direction
m2: magnitude m/s2
direction
m3: magnitude m/s2
direction

Explanation / Answer

A for m1 is down for m2 is to the left and m3 is up

Free body diagrams about each yields

m1*g - Tleft = m1*a so T (left) = m1*g - m1*a

T (left) - T (right) - %u03BC*m2*g = m2*a

T (right) - m3*g = m3*a So T (right) = m3*g + m3*a

Now sub the first and third into the second

m1*g - m1*a - m3*a - m3*g - %u03BC*m2*g = m2a

So (m1 + m2 + m3)*a = g*(m1 - m3 - %u03BC*m2)

So a = g*(m1- m3 - %u03BC*m2) /(m1 + m2 + m3) = 9.8*(3.750 - 2.40 - 0.37*1.5)/(3.750 + 1.5 + 2.4)

= 1.018 m/s^2 The directions were given above

Now T (left) = m1*g - m1*a = 3.750*(9.8 - 1.018) = 32.9N

T (right) = m3*g + m3*a = 2.40*(9.8 + 1.018) = 21.07N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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