Question

step 6: calculate the pre... of the falling soda bottles
in this part of the experiment, you will be cha speed of the bottle by dropping it from differe you will use the same mass, 0.250 kg, for ea record this mass in table b for each velocity. calculate the expected kinetic energy (ke) at velocity. use the formula $ke = \frac{1}{2}mv^2$,
where m is the mass and v is the speed. rec calculations in table b of your student guide.
when the speed of the bottle is 2 m/s, the ke is
when the speed of the bottle is 3 m/s, the ke is
when the speed of the bottle is 4 m/s, the ke is
when the speed of the bottle is 5 m/s, the ke is dropdown with 3,5,6,7 kg·m²/s².
when the speed of the bottle is 6 m/s, the ke is dropdown kg·m²/s².

Explanation:

Step1: Identify formula and values

Given \( KE = \frac{1}{2}mv^2 \), \( m = 0.250 \, \text{kg} \), \( v = 5 \, \text{m/s} \) (first case) and \( v = 6 \, \text{m/s} \) (second case).

Step2: Calculate KE for \( v = 5 \, \text{m/s} \)

Substitute \( m = 0.250 \) and \( v = 5 \) into the formula:
\( KE = \frac{1}{2} \times 0.250 \times (5)^2 \)
\( = \frac{1}{2} \times 0.250 \times 25 \)
\( = 0.125 \times 25 \)
\( = 3.125 \, \text{kg·m}^2/\text{s}^2 \)

Step3: Calculate KE for \( v = 6 \, \text{m/s} \)

Substitute \( m = 0.250 \) and \( v = 6 \) into the formula:
\( KE = \frac{1}{2} \times 0.250 \times (6)^2 \)
\( = \frac{1}{2} \times 0.250 \times 36 \)
\( = 0.125 \times 36 \)
\( = 4.5 \, \text{kg·m}^2/\text{s}^2 \)

Answer:

When the speed is 5 m/s, KE is \( 3.125 \, \text{kg·m}^2/\text{s}^2 \); when the speed is 6 m/s, KE is \( 4.5 \, \text{kg·m}^2/\text{s}^2 \).