In a physics lab experiment, a spring clamped to the table shoots a 18 g ball horizontally. When the spring is compressed 20 cm, the ball travels horizontally 4.9 m and lands on the floor 1.3 m below the point at which it left the spring. What is the spring constant?
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = -k * x
where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement of the spring from its equilibrium position.
In this case, we need to find the spring constant, given that the ball travels horizontally 4.9 m.
When the spring is compressed by 20 cm (or 0.2 m), it generates a force that propels the ball horizontally. The horizontal distance covered by the ball is 4.9 m.
The vertical displacement of the ball is given by 1.3 m.
To find the spring constant, we need to consider the horizontal motion of the ball. In horizontal motion, there is no acceleration due to gravity, so the force exerted by the spring is equal to the force required to overcome air resistance.
We can calculate the force required to overcome air resistance using Newton's second law:
F = m * a
Since the mass of the ball is given as 18 g (or 0.018 kg) and there is no acceleration in horizontal motion, the force can be calculated as:
F = 0.018 kg * 0 = 0 N
Now, we can use Hooke's Law to equate the force exerted by the spring to the force required to overcome air resistance:
-k * x = 0
Solving for k, we find:
k = 0
Therefore, the spring constant in this case is 0.