A cart of mass 0.68 kg is attached to one end of of a spring and placed on a low-friction track, inclined at an angle of 61.5 degrees with respect to the horizontal. The cart is found to be in equilibrium when the spring is stretched to a total length of 52.0 cm. Given that the rest length for the spring is 12 cm, what is the spring constant for the spring

The value is

Explanation:

From the question we are told that

The mass of the cart is  m  =  0.68 kg

The angle of inclination is

The length of the spring when the cart is a equilibrium is  

The length of the spring when at rest is  

Generally the weight of the cart is mathematically represented as

=>    

=>    

Generally the force applied on the spring by the weight of the cart is mathematically represented as

So at equilibrium

=>  

=>  

=>