A vertical spring (ignore its mass), whose spring constant is 900 N/m, id attached to a table and is compressed 0.150 m. What speed can it give to a 0.300-kg ball when released? How high above its original position (spring compressed) will the ball fly?
To find the speed that the ball will have when released, we can use the conservation of mechanical energy. The potential energy stored in the compressed spring will be converted into kinetic energy of the ball.
The potential energy stored in a spring is given by the equation:
PE = 0.5 * k * x^2
Where PE is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, the potential energy stored in the spring is:
PE = 0.5 * 900 N/m * (0.150 m)^2 = 20.25 J
This potential energy will be converted into kinetic energy of the ball when released. The kinetic energy of an object is given by the equation:
KE = 0.5 * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
Setting the potential energy equal to the kinetic energy, we can solve for the velocity:
20.25 J = 0.5 * 0.3 kg * v^2
v^2 = 135 J/kg
v ≈ 11.62 m/s
Therefore, the speed that the ball will have when released is approximately 11.62 m/s.
To find the height that the ball will reach above its original position, we can use the conservation of energy. The initial potential energy stored in the spring will be converted into potential energy of the ball at its maximum height.
The potential energy of an object above the ground is given by the equation:
PE = m * g * h
Where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the ground.
Setting the initial potential energy equal to the potential energy at maximum height, we can solve for h:
20.25 J = 0.3 kg * 9.8 m/s^2 * h
h = 20.25 J / (0.3 kg * 9.8 m/s^2)
h ≈ 22.11 m
Therefore, the ball will reach a height of approximately 22.11 m above its original position (spring compressed).