Question

you drop two balls from a tower, one of mass m and the other of mass 3m.
Just before they hit the ground, which ball, if either, has the larger kinetic energy?

a. second
b. first
c. both balls have the same kinetic energy

Answer 1

The potential energy that the ball has at the top of the tower is its kinetic energy when it hits the ground. The second ball has more potential energy at the top, because you did more work on it to carry it up there. So it has more KE at the bottom. (A)

Answer 2

a. Second ball of mass 3m has the larger kinetic energy than the first ball of mass m

$\texttt{ }$

Further explanation

Let's recall the Kinetic Energy formula:

$\boxed {E_k = \frac{1}{2}mv^2 }$

Ek = kinetic energy ( J )

m = mass of object ( kg )

v = speed of object ( m/s )

$\texttt{ }$

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

$\texttt{ }$

Given:

mass of first ball = m

mass of second ball = 3m

Asked:

ratio of kinetic energy of the balls = Ek₁ : Ek₂ = ?

Solution:

$Ek_1 : Ek_2 = \frac{1}{2}m_1 v_1^2 : \frac{1}{2}m_2 v_2^2$

$Ek_1 : Ek_2 = \frac{1}{2}m_1 (2gh) : \frac{1}{2}m_2 (2gh)$

$Ek_1 : Ek_2 = m_1gh : m_2gh$

$Ek_1 : Ek_2 = m_1 : m_2$

$Ek_1 : Ek_2 = m : 3m$

$Ek_1 : Ek_2 = 1 : 3$

$Ek_2 = 3Ek_1$

$\texttt{ }$

Conclusion:

Second ball of mass 3m has the larger kinetic energy than the first ball of mass m

$\texttt{ }$

Learn more

• Velocity of Runner : https://brainly.com/question/3813437

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302

$\texttt{ }$

Answer details

Grade: High School

Subject: Mathematics

Chapter: Energy