Answer: 3661.3 N/m
Explanation:
we can solve the problem by using the law of conservation of energy.
Initially, all the energy of the system is stored as elastic potential of the spring, which is given by
[tex]E_p = \frac{1}{2}kx^2[/tex]
where k is the spring constant and x=1.69 cm=0.0169 m is the compression of the spring.
Later, when the spring is released, all the energy is converted into gravitational potential energy of the toy, which at its highest point is equal to
[tex]E_g=mgh[/tex]
where m=104 g=0.104 kg is the mass of the toy, g=9.8 m/s^2 is the acceleration of gravity, and h=51.3 cm=0.513 m is the height reached by the toy.
Using the conservation of energy, we can write:
[tex]\frac{1}{2}kx^2=mgh[/tex]
[tex]k=\frac{2mgh}{x^2}=\frac{2(0.104 kg)(9.8 m/s^2)(0.513 m)}{(0.0169 m)^2}=3661.3 N/m[/tex]
