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
