Answer:
Step-by-step explanation:
We can use the conservation of energy principle to find the force constant of the spring. Initially, the ball has potential energy due to its height above the spring, and no kinetic energy. When it strikes the spring, it compresses it, and its potential energy is converted to elastic potential energy in the spring. At the instant the ball comes to rest, all of its initial potential energy has been converted to elastic potential energy in the spring.
The potential energy of the ball at height h is given by:
U = mgh
Where m is the mass of the ball, g is the acceleration due to gravity, and h is the initial height of the ball.
The elastic potential energy stored in the spring when it is compressed by distance d is given by:
U = (1/2)kx^2
where k is the force constant of the spring, and x is the compression distance.
Since the potential energy of the ball is converted entirely to elastic potential energy in the spring, we can set these two expressions equal to each other:
mgh = (1/2)kx^2
Plugging in the given values, we have:
m = 1.55 kg
g = 9.81 m/s^2
h = 0.68 m
d = 0.091 m
Substituting these values into the equation, we get:
(1.55 kg)(9.81 m/s^2)(0.68 m) = (1/2)k(0.091 m)^2
Solving for k, we get:
k = (2mgh)/(d^2) = 2365 N/m
Therefore, the force constant of the spring is 2365 N/m.