Question

Suppose the angles shown in the figure are 70 ∘ and 18 ∘. (Figure 1)

Part A If the left-hand mass is 2.6 kg ,what should the right-hand mass be so that it accelerates downslope at 0.64 m/s2? What should the right-hand mass be so that it accelerates upslope at 0.76 m/s2?

Answer 1

for block m₁ , force equation parallel to incline is given as

T - m₁ g Sin70 = m₁ a

T - (2.6) (9.8) Sin70 = 2.6 (0.64)

T = 25.61 N

for the block m₂ , force equation is given as

m₂ g Sin18 - T = m₂ a

m₂ (9.8) Sin18 - 25.61 = m₂ (0.64)

m₂ = 10.7 kg

b)

when right block moves upslope,

for block m₁ , force equation parallel to incline is given as

m₁ g Sin70 - T = m₁ a

(2.6) (9.8) Sin70 - T = 2.6 (0.76)

T = 21.97 N

for the block m₂ , force equation is given as

T - m₂ g Sin18 = m₂ a

21.97 - m₂ (9.8) Sin18 = m₂ (0.76)

m₂ = 5.8 kg