Question

two balls of different masses are rolled down a hill at different velocities. they data of these events are recorded below.
mass (g)
ball 1 trial 1: 50, ball 1 trial 2: 50, ball 2 trial 1: 100, ball 2 trial 2: 100
velocity (m/s)
ball 1 trial 1: 2, ball 1 trial 2: 4, ball 2 trial 1: 2, ball 2 trial 2: 4

1. did ball 1 have more kinetic energy in trial 1 or in trial 2.

trial 1
trial 2

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the velocity.

Step2: Calculate kinetic energy for Ball 1 in Trial 1

For Ball 1 in Trial 1, $m = 50g=0.05kg$ and $v = 2m/s$. Then $KE_1=\frac{1}{2}\times0.05\times2^{2}=\frac{1}{2}\times0.05\times4 = 0.1J$.

Step3: Calculate kinetic energy for Ball 1 in Trial 2

For Ball 1 in Trial 2, $m = 50g = 0.05kg$ and $v = 4m/s$. Then $KE_2=\frac{1}{2}\times0.05\times4^{2}=\frac{1}{2}\times0.05\times16=0.4J$.

Step4: Compare the kinetic energies

Since $0.4J>0.1J$, Ball 1 has more kinetic energy in Trial 2.

Answer:

Trial 2