Achild’s toy consists of plastic attached to a spring. the spring is compressed against the floor a distance of 1.69 cm, and the toy is released. the acceleration of gravity is 9.8 m/ s^2. if the toy has a mass of 104 g and rises to a maximum height of 51.3 cm, estimate the force constant of the spring. answer in units of n/m.

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

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

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:

be subject to a force andchange its motion