In compressed state, a spring 3.00 meters long hanging from the ceiling has a potential energy of 2.0 joules. If the entire potential energy is used to release a ball of mass 1.2 kilograms vertically downward, then what is the kinetic energy of the ball when it reaches the ground?
1.2 joules
4.9 joules
2.0 joules
6.8 joules
4.9
4.9j
To find the kinetic energy of the ball when it reaches the ground, we need to apply the principle of conservation of energy. According to this principle, the total energy remains constant throughout the process.
1. First, let's calculate the potential energy stored in the compressed spring. The potential energy (PE) can be calculated using the formula PE = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position.
Since the spring is 3.00 meters long, we know that the displacement is 3.00 meters when it's compressed. Given that the potential energy is 2.0 joules, we can set up the equation:
2.0 joules = (1/2)k(3.00 meters)^2
Next, we need to solve for the spring constant (k). Rearranging the equation, we have:
k = (2 * 2.0 joules) / (3.00 meters)^2
k = 8.0 joules/meter^2
2. Next, we can calculate the gravitational potential energy (PE_gravity) of the ball when it reaches the ground. The gravitational potential energy can be calculated using the formula PE_gravity = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
From the problem, we know that the height is 3.00 meters (since the spring is 3.00 meters long). Therefore, we can calculate the gravitational potential energy:
PE_gravity = (1.2 kg) * (9.8 m/s^2) * (3.00 meters)
PE_gravity = 35.28 joules
3. Now, since the total energy is conserved, the potential energy stored in the spring is equal to the gravitational potential energy of the ball. Therefore, the kinetic energy (KE) of the ball when it reaches the ground can be calculated by subtracting the potential energy (2.0 joules) from the gravitational potential energy (35.28 joules):
KE = PE_gravity - PE
KE = 35.28 joules - 2.0 joules
KE = 33.28 joules
So, the kinetic energy of the ball when it reaches the ground is approximately 33.28 joules.
To find the kinetic energy of the ball when it reaches the ground, we need to apply the principle of conservation of energy. According to this principle, the total energy of the system (spring and ball) remains constant.
At the compressed state, the potential energy of the spring is 2.0 joules. This potential energy is transformed into the kinetic energy of the ball when it is released.
The potential energy of the spring can be converted to the kinetic energy of the ball using the formula:
Potential Energy = Kinetic Energy
We can rearrange this formula to solve for the kinetic energy:
Kinetic Energy = Potential Energy
The potential energy of the spring is given as 2.0 joules.
Therefore, the kinetic energy of the ball when it reaches the ground will also be 2.0 joules.
So, the correct answer is 2.0 joules.