Question

What is the speed of the silver sphere at the moment it hits the ground? (Assume that energy is conserved during the fall and that 100% of the sphere’s initial potential energy is converted to kinetic energy by the time impact occurs.)

Answer 1

Complete question:

Consider the two spheres shown here, one made of silver and the other of aluminum. The spheres are dropped from a height of 2.1 m. (composition of sphere : density is 10.49 g/cm³, volume is 196 cm³), (composition of aluminum : density is 2.7 g/cm³, volume is 196 cm³).

What is the speed of the silver sphere at the moment it hits the ground? (Assume that energy is conserved during the fall and that 100% of the sphere’s initial potential energy is converted to kinetic energy by the time impact occurs.)

Answer:

The speed of the silver sphere at the moment it hits the ground is 6.416 m/s

Explanation:

Potential energy of the silver sphere = mgh

where;

g is acceleration due to gravity = 9.8 m/s²

h is height above the ground = 2.1m

m is mass of the silver sphere =?

Density = mass/volume

mass of the silver sphere = density X volume = (10.49 g/cm³) X (196cm³ )

mass of the silver sphere = 2056.04 g = 2.056 kg

Potential energy of the silver sphere =  (2.056 X 9.8 X 2.1) J

Potential energy of the silver sphere = 42.31248 J

If energy is conserved and 100% potential energy is converted to kinetic energy, the speed of the silver sphere will be calculated as follows:

Kinetic Energy (K.E) = 1/2mv²

where;

m is mass of the sphere in kg = 2.056kg

v is the velocity of the silver sphere = ?

If energy is conserved; Potential energy = Kinetic energy

42.31248 = 1/2mv²

v² = (42.31248 X 2)/m

v² = (42.31248 X 2)/2.056

v² = 41.16

v = √41.16

v = 6.416 m/s

Therefore, the speed of the silver sphere at the moment it hits the ground is 6.416 m/s