Question

step 3: calculate the predicted change in kinetic energy
calculate the change in the kinetic energy (ke) of the bottle when the mass is increased. use the formula ( ke = \frac{1}{2}mv^2 ), where ( m ) is the mass and ( v ) is the speed (velocity). assume that the speed of the soda bottle falling from a height of 0.8 m will be 4 m/s, and use this speed for each calculation.
record your calculations in table a of your student guide.
when the mass of the bottle is 0.125 kg, the ke is 1 ( \text{kg} cdot \text{m}^2/\text{s}^2 ).
when the mass of the bottle is 0.250 kg, the ke is 2 ( \text{kg} cdot \text{m}^2/\text{s}^2 ).
when the mass of the bottle is 0.375 kg, the ke is (options: 3, 3.75, 6, 9) ( \text{kg} cdot \text{m}^2/\text{s}^2 ).
when the mass of the bottle is 0.500 kg, the ke is...

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass (in kg) and \( v \) is the speed (in m/s). We know \( v = 4 \, \text{m/s} \) and for this case, \( m = 0.375 \, \text{kg} \).

Step2: Substitute the values into the formula

Substitute \( m = 0.375 \) and \( v = 4 \) into \( KE = \frac{1}{2}mv^2 \). First, calculate \( v^2 \): \( 4^2 = 16 \). Then, multiply by \( m \): \( 0.375 \times 16 = 6 \). Then, multiply by \( \frac{1}{2} \): \( \frac{1}{2} \times 6 = 3 \)? Wait, no, wait. Wait, \( \frac{1}{2} \times 0.375 \times 16 \). Let's compute that again. \( 0.375 \times 16 = 6 \), then \( \frac{1}{2} \times 6 = 3 \)? Wait, no, maybe I made a mistake. Wait, \( \frac{1}{2} \times 0.375 \times 4^2 \). \( 4^2 = 16 \), \( \frac{1}{2} \times 16 = 8 \), then \( 0.375 \times 8 = 3 \)? Wait, no, 0.375 is \( \frac{3}{8} \), so \( \frac{3}{8} \times 8 = 3 \). Wait, but let's check again. Wait, the formula is \( KE = 0.5 \times m \times v^2 \). So \( m = 0.375 \), \( v = 4 \). So \( 0.5 \times 0.375 \times 16 \). 0.5 times 16 is 8, 8 times 0.375 is 3. Wait, but the options include 3, 3.75, 6, 9. Wait, maybe I messed up the mass? Wait, no, the mass is 0.375 kg. Wait, let's recalculate: \( \frac{1}{2} \times 0.375 \times 4^2 = 0.5 \times 0.375 \times 16 = 0.5 \times 6 = 3 \). Wait, but let's check the other masses. For 0.125 kg: \( 0.5 \times 0.125 \times 16 = 0.5 \times 2 = 1 \), which matches the first value. For 0.250 kg: \( 0.5 \times 0.250 \times 16 = 0.5 \times 4 = 2 \), which matches the second value. So for 0.375 kg: \( 0.5 \times 0.375 \times 16 = 0.5 \times 6 = 3 \). So the answer should be 3.

Answer:

3