A student places her 330 g physics book on a frictionless table. She pushes the book against a spring, compressing the spring by 9.90 cm, then releases the book
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. The equation for Hooke's Law is given by:
F = -k * x
Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.
In this case, the displacement of the spring is given as 9.90 cm or 0.099 m. We need to determine the force exerted by the spring.
We're also given the mass of the book, which is 330 g or 0.33 kg. We know that the force exerted by the spring is equal to the weight of the book when the book is in equilibrium.
The weight of an object is given by the equation:
F = m * g
Where:
F is the force or weight,
m is the mass, and
g is the acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s^2.
Substituting the values into the equation, we find:
F = 0.33 kg * 9.8 m/s^2
F = 3.234 N
Now that we have the force exerted by the spring, we can use Hooke's Law to find the spring constant.
3.234 N = -k * 0.099 m
Rearranging the equation, we get:
k = -3.234 N / 0.099 m
k ≈ -32.67 N/m
The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.
Therefore, the spring constant for this system is approximately -32.67 N/m.