Question

1. (01.04 hc)

explain how the energy of a toy car is transformed as it slides down a ramp. give evidence that the energy of the car remains the same at all points on the ramp.

Explanation:

1. Energy Transformation: At the top of the ramp, the toy car has gravitational potential energy (GPE) due to its height ($GPE = mgh$, where $m$ is mass, $g$ is gravity, $h$ is height). As it slides down, height decreases, so GPE decreases. Simultaneously, the car’s speed increases, so kinetic energy ($KE=\frac{1}{2}mv^{2}$, $m$=mass, $v$=velocity) increases. Thus, GPE transforms into KE (and some thermal energy due to friction, but for idealized cases, we focus on mechanical energy).
2. Energy Conservation (Evidence): In a closed system (ignoring friction for simplicity), mechanical energy (sum of GPE and KE) is conserved. At any point on the ramp, calculate $GPE + KE$. At the top: $GPE_{top}=\ mgh_{top}$, $KE_{top} = 0$ (starts from rest), so total energy $E_{top}=mgh_{top}$. At a lower point (height $h_{lower}$), $GPE_{lower}=mgh_{lower}$ and $KE_{lower}=\frac{1}{2}mv_{lower}^{2}$. From conservation of energy (or kinematics: $v^{2}=2g(h_{top}-h_{lower})$), substituting gives $KE_{lower}=mg(h_{top}-h_{lower})$, so $E_{lower}=mgh_{lower}+mg(h_{top}-h_{lower})=mgh_{top}=E_{top}$. Even with friction, the total energy (mechanical + thermal) remains constant (law of conservation of energy), so the “energy of the car” (mechanical, or total) is conserved in a closed system.

Answer:

• Energy Transformation: The toy car’s gravitational potential energy (GPE, due to height) decreases as it slides down the ramp, while its kinetic energy (KE, due to speed) increases. Thus, GPE transforms into KE (and some thermal energy due to friction).
• Evidence of Energy Conservation: In an ideal system (no friction), the total mechanical energy (GPE + KE) remains constant. At the top, $E = GPE = mgh$ (KE = 0, since it starts from rest). At any lower point, $GPE$ decreases by $mg\Delta h$ (where $\Delta h$ is the height lost), and $KE$ increases by $\frac{1}{2}mv^{2}=mg\Delta h$ (from kinematics, $v^{2}=2g\Delta h$). Thus, $GPE + KE$ at any point equals $mgh$ (the initial energy). Even with friction, the total energy (mechanical + thermal) remains constant (law of conservation of energy), so the car’s total energy is conserved.