Question

1. how much energy is there in each one of these scenarios? (remember to use si units when using physics form

scenarios
a truck moving very slow
mass: 16000 kg
velocity: \\(\frac{5}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \frac{1}{2}mv^2 = \\)
a car moving fast
mass: 1500kg
velocity: \\(\frac{50}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a girl riding with a scooter
girl: 20 kg, scooter:3kg
velocity: \\(\frac{3}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a wrecking ball
mass: 2000 kg
velocity: \\(\frac{14}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a bullet being shot
mass: 4 g
velocity: \\(\frac{1000}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a baseball that was just hit
mass: 149 g
velocity: \\(\frac{10}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a modern locomotive
mass: \\(6.4 \cdot 10^5\\) kg
velocity: \\(\frac{1}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)
a motorist at a traffic light
motorist:70kg, motorbike: 300kg
velocity: \\(\frac{0}{m}\\)\\(\frac{m}{s}\\)
\\(e_k = \\)

Explanation:

Step1: Recall kinetic energy formula

The kinetic energy formula is $E_k = \frac{1}{2}mv^2$, where $m$ = mass (in kg), $v$ = velocity (in $\frac{m}{s}$).

Step2: Calculate for slow truck

Convert mass to kg (already 16000 kg), substitute values:
$E_k = \frac{1}{2} \times 16000 \times 5^2 = \frac{1}{2} \times 16000 \times 25 = 200000$ J

Step3: Calculate for fast car

Substitute $m=1500$ kg, $v=50$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 1500 \times 50^2 = \frac{1}{2} \times 1500 \times 2500 = 1875000$ J

Step4: Calculate for girl+scooter

Total mass $m=20+3=23$ kg, $v=3$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 23 \times 3^2 = \frac{1}{2} \times 23 \times 9 = 103.5$ J

Step5: Calculate for wrecking ball

Substitute $m=2000$ kg, $v=14$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 2000 \times 14^2 = \frac{1}{2} \times 2000 \times 196 = 196000$ J

Step6: Calculate for bullet

Convert mass: $4$ g = $0.004$ kg, $v=1000$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 0.004 \times 1000^2 = \frac{1}{2} \times 0.004 \times 1000000 = 2000$ J

Step7: Calculate for baseball

Convert mass: $149$ g = $0.149$ kg, $v=10$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 0.149 \times 10^2 = \frac{1}{2} \times 0.149 \times 100 = 7.45$ J

Step8: Calculate for locomotive

Substitute $m=6.4 \times 10^5$ kg, $v=1$ $\frac{m}{s}$:
$E_k = \frac{1}{2} \times 6.4 \times 10^5 \times 1^2 = 3.2 \times 10^5 = 320000$ J

Step9: Calculate for stopped motorist

Velocity $v=0$ $\frac{m}{s}$, total mass $m=70+300=370$ kg:
$E_k = \frac{1}{2} \times 370 \times 0^2 = 0$ J

Answer:

1. Slow truck: $200000$ J
2. Fast car: $1875000$ J
3. Girl + scooter: $103.5$ J
4. Wrecking ball: $196000$ J
5. Shot bullet: $2000$ J
6. Hit baseball: $7.45$ J
7. Modern locomotive: $320000$ J
8. Stopped motorist: $0$ J