A lift of mass 1600 kg is supported by a thick iron wire. If the maximum stress which the wire can withstand is 4×10⁸ N m⁻² and its radius is 4 mm, then the maximum acceleration the lift can take is m s⁻². (Take g=10 m s⁻² and π=3.14)

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(1) 2.56. Given: m=1600 kg, σₘₐₓ=4×10⁸ N m⁻², r=4 mm=4×10⁻³ m. A=π r²=3.14×(4×10⁻³)²=5.024×10⁻⁵ m². The largest tension the wire can take is Tₘₐₓ=σₘₐₓA=4×10⁸×5.024×10⁻⁵=2.0096×10⁴ N. For a lift accelerating upward, T=m(g+a), so g+a=(2.0096×10⁴)/(1600)=12.56 m s⁻². a=12.56-10=2.56 m s⁻².

A lift of mass 1600 kg is supported by a thick iron wire. If the maximum stress which the wire can withstand is 4×10⁸ N m⁻² and its radius is 4 mm, then the maximum acceleration the lift can take is ______ m s⁻². (Take g=10 m s⁻² and π=3.14)

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