In Figure 5-49, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude T3 = 64.0 N.

Question

In Figure 5-49, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude T3 = 64.0 N.

Figure 5-49 (Image Address http://www.webassign.net/hrw/05_47.gif )

(a) If m1 = 12.5 kg, m2 = 24.7 kg, and m3 = 31.0 kg, calculate the magnitude of the acceleration of the system.

(b) Calculate the tension T1

(c) Calculate the tension T2.

Answer 1

For all three parts, use Newton's second law, F = ma.

(a) The total mass of the system is

m = m₁+m₂+m₃ = 12.5 kg + 24.7 kg + 31.0 kg = 68.2 kg

so the acceleration is

a = T₁/m = (64.0 N) / (68.2 kg) = 0.938 m/s².

(b) T₁ = m₁a = (12.5 kg)(0.938 m/s²) = 11.7 N

(c) T₂ = (m₁+m₂)a = (12.5 kg + 24.7 kg)(0.938 m/s²)

    = (37.2 kg)(0.938 m/s²) = 34.9 N