Question

all carts shown below are identical, 0.5 kg metal carts. blocks placed in the carts have a mass of 1.0 kg each. in which arrangement does the cart have the least amount of potential energy when it is at the top of the ramp?

Explanation:

Step1: Recall gravitational PE formula

Gravitational potential energy is given by $PE = mgh$, where $m$ is total mass, $g$ is acceleration due to gravity, and $h$ is height of the object's center of mass (here, the height of the ramp top is the same for all, so $h$ is constant across all options; $g$ is also constant).

Step2: Calculate total mass for each option

• Option A: $m_A = 0.5\ \text{kg} + (2 \times 1.0\ \text{kg}) = 2.5\ \text{kg}$
• Option B: $m_B = 0.5\ \text{kg} + (3 \times 1.0\ \text{kg}) = 3.5\ \text{kg}$
• Option C: $m_C = 0.5\ \text{kg} + (3 \times 1.0\ \text{kg}) = 3.5\ \text{kg}$
• Option D: $m_D = 0.5\ \text{kg} + (1 \times 1.0\ \text{kg}) = 1.5\ \text{kg}$

Step3: Compare PE values

Since $PE \propto m$ (as $g$ and $h$ are constant), the smallest total mass gives the least potential energy.

Answer:

D. The cart with 1 block (total mass 1.5 kg) at the top of the ramp