1) 1) A spring has a length of 0.258 m when a 0.300 kg mass hangs from it, and a

Question

1)

1) A spring has a length of 0.258 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.82 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.)
N/m

(b) What is the unloaded length of the spring?
m

2)An athlete with a mass of 55.5 kg is in a cross country race, and at one instant he has a speed of 5.60 m/s.

Explanation / Answer

Q1. Force acting on the spring F=-kx; where k is the spring constant and x is the displacement

Let us consider the unloaded length of spring as x0

Therefore we get F=k*(0.258-x0)=0.30g and F=k*(0.750-x0)=2.82g

Soving the above two equations we get the unloaded length of spring x0=0.199 m (say 0.20 m)

Again using the value of x0 and putting in the above equations we get force constant k= 50.74 N/m

Q2. Kinetic Energy E =1/2(mv2)

In the particular problem E=1/2*55.5*5.602= 870.24 Joules

Since Kinetic Energy is proportional to square of velocity, hence by doubling the speed the kinetic energy will increase by a factor of 4.

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