Consider the two spheres shown here, one made of silver and the other of aluminum. (d) If you release the spheres simultaneously, they will have the same velocity when they hit the ground. Will they have the same kinetic energy? If not, which sphere will have more kinetic energy?

Verified step by step guidance

1. Understand that kinetic energy (KE) is given by the formula: \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass and \( v \) is the velocity.
2. Since both spheres are released simultaneously and fall under the influence of gravity, they will have the same velocity \( v \) when they hit the ground.
3. The kinetic energy of each sphere depends on both its mass and the velocity it has when it hits the ground.
4. To determine which sphere has more kinetic energy, compare their masses. The sphere with the greater mass will have more kinetic energy, as \( v \) is the same for both.
5. Consider the densities of silver and aluminum. Silver is denser than aluminum, so for spheres of the same size, the silver sphere will have a greater mass and thus more kinetic energy when they hit the ground.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. Although both spheres will have the same velocity upon hitting the ground, their kinetic energies will differ because kinetic energy is also dependent on mass.

Mass and Weight

Mass is a measure of the amount of matter in an object, while weight is the force exerted by gravity on that mass. In this scenario, the silver sphere has a greater mass than the aluminum sphere, which means it will have a higher weight and, consequently, more kinetic energy when both are dropped from the same height.

Acceleration due to Gravity

Acceleration due to gravity is a constant value (approximately 9.81 m/s² on Earth) that affects all objects regardless of their mass. When both spheres are released, they accelerate towards the ground at the same rate, ensuring they reach the same velocity just before impact, but this does not influence their kinetic energy, which is also dependent on their respective masses.