Question

1. which would increase the kinetic energy of a wagon? select all that apply.

□ a) add mass to the wagon.
□ b) decrease the mass of the wagon.
□ c) increase the speed of the wagon.
□ d) decrease the speed of the wagon.

1. a dump truck, a sports car, and a bicycle are traveling at the same velocity. which is true?

○ a) they all have the same kinetic energy.
○ b) the sports car has the most kinetic energy.
○ c) the bicycle has the least kinetic energy.
○ d) more information is needed to compare their kinetic energy.

Explanation:

Question 4

Step1: Recall Kinetic Energy Formula

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

Step2: Analyze Option A

If we add mass ($m$ increases) to the wagon, from $KE = \frac{1}{2}mv^2$, since $v$ (assuming it stays same or we are just considering mass effect) and $\frac{1}{2}$ is constant, increasing $m$ will increase $KE$. So A is correct.

Step3: Analyze Option B

Decreasing mass ($m$ decreases) will decrease $KE$ (from $KE = \frac{1}{2}mv^2$), so B is incorrect.

Step4: Analyze Option C

Increasing speed ($v$ increases), from $KE = \frac{1}{2}mv^2$, since $m$ (assuming constant) and $\frac{1}{2}$ is constant, increasing $v$ (squared term) will increase $KE$. So C is correct.

Step5: Analyze Option D

Decreasing speed ($v$ decreases) will decrease $KE$ (from $KE = \frac{1}{2}mv^2$), so D is incorrect.

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$. Here, velocity ($v$) is the same for all three (dump truck, sports car, bicycle).

Step2: Analyze Masses

A dump truck has a large mass, a sports car has a moderate mass, and a bicycle has a small mass. Since $KE$ is proportional to mass ($KE \propto m$ when $v$ is constant), the object with the least mass will have the least kinetic energy. The bicycle has the least mass among the three.

Step3: Evaluate Options

• Option A: False, because masses are different, so $KE$ can't be same.
• Option B: False, dump truck has more mass than sports car, so dump truck has more $KE$ than sports car.
• Option C: True, bicycle has least mass, so least $KE$.
• Option D: False, we can compare using $KE = \frac{1}{2}mv^2$ (we know $v$ is same, just need to compare masses).

Answer:

A) Add mass to the wagon, C) Increase the speed of the wagon

Question 5