Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen for equal times, we find that
A)KB = KA.
B)KB = 2KA.
C)KB = 4KA.
D)KA = 2KB.
E)KA = 4KB.

Question

Quizplus · Accepted Answer

The kinetic energy of an object is given by KE = (1/2)mv^2, where m is the mass and v is the velocity. Since both objects are falling straight down, they have the same acceleration due to gravity, which is -9.8 m/s^2.

Using the equations of motion, we can find the velocity of each object after falling for a certain time t:

vA = -9.8t 
vB = -9.8t

Since MB = 2MA, the mass is twice as much for object B. Plugging in the velocity and mass for each object, we get:

KA = (1/2)(MA)(-9.8t)^2 = 4.9MAt^2 
KB = (1/2)(MB)(-9.8t)^2 = 19.6MAt^2

Therefore, we have KB = 2KA. So the correct choice is B.

Two Masses, MA and MB, with MB = 2MA, Are