Question

kinetic energy, mass, and velocity #1
use kinematics equations to solve the problems below.

1. a 2300-kg truck is traveling down a highway at 32 m/s. what is the kinetic energy of the truck?

1. a 58-kg boy swings a baseball bat, which causes a 0.140-kg baseball to move towards third base with a velocity of 38.0 m/s. what it the kinetic energy of the baseball?

1. a 35-kg boy is riding an 18-kg bicycle down a path. if the bicycle is moving at 11 m/s, what is the kinetic energy of the boy and the bicycle?

1. does a 0.14 kg baseball moving at 41 m/s or a 0.058-kg tennis ball moving at 67 m/s have more kinetic energy?

Explanation:

Problem 1

Step1: Recall kinetic energy formula

The formula for kinetic energy ($KE$) is $KE = \frac{1}{2}mv^2$, where $m$ is mass in kilograms and $v$ is velocity in meters per second.

Step2: Identify values for the truck

For the truck, $m = 2300\space kg$ and $v = 32\space m/s$.

Step3: Substitute into the formula

$KE=\frac{1}{2}\times2300\times(32)^2$
First, calculate $(32)^2 = 1024$.
Then, $\frac{1}{2}\times2300 = 1150$.
Now, multiply $1150\times1024 = 1177600\space J$.

Step1: Recall kinetic energy formula

$KE = \frac{1}{2}mv^2$

Step2: Identify values for the baseball

$m = 0.140\space kg$, $v = 38.0\space m/s$

Step3: Substitute into the formula

$KE=\frac{1}{2}\times0.140\times(38.0)^2$
Calculate $(38.0)^2 = 1444$.
$\frac{1}{2}\times0.140 = 0.07$.
Multiply $0.07\times1444 = 101.08\space J$.

Step1: Recall kinetic energy formula

$KE = \frac{1}{2}mv^2$, where $m$ is the total mass of the boy and the bicycle.

Step2: Calculate total mass

Total mass $m = 35 + 18 = 53\space kg$, and $v = 11\space m/s$.

Step3: Substitute into the formula

$KE=\frac{1}{2}\times53\times(11)^2$
Calculate $(11)^2 = 121$.
$\frac{1}{2}\times53 = 26.5$.
Multiply $26.5\times121 = 3206.5\space J$.

Answer:

The kinetic energy of the truck is $1177600\space J$ (or $1.1776\times10^{6}\space J$).

Problem 2