A spring has a length of 0.288 m when a 0.300 kg mass hangs from it, and a lengt

Question

A spring has a length of 0.288 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.92 kg mass hangs from it. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) What is the force constant of the spring? (Use 9.8 m/s2 for g.) See if you can write an equilibrium statement for the case when the mass m is suspended from the spring and it is stretched to a total length /1. In like manner, see if you can write an equilibrium statement for the case when the mass m2 is suspended from the spring and it is stretched to a total length /2. See if you can combine these two equilibrium statements to determine an expression for the force constant of the spring. N/m (b) What is the unloaded length of the spring? Additional Materials Reading Tutorial

Explanation / Answer

Net force

F = g(m2-m1)= 9.8*(2.90-0.3)= 25.48 N

Net displacement, d= 0.75-0.288 m

Spring constant,

K= F/d= 25.48/(0.75-0.288)= 55.152 N/m

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x= f/k= 0.3*9.8/55.152= 0.0533

Length of spring

L= 0.288-0-0533

= 0.2347 m

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