Question

the image shows two carts (cart a: 4 kg, cart b: 8 kg) connected by a compressed spring. when the spring is released, it pushes the carts apart with equal force. if the spring’s stored energy is released (sending carts opposite directions), which cart travels farther? options: cart a (least mass); cart b (most mass); cart b (more volume); cart a (least volume).

Explanation:

To determine which cart travels farther, we use Newton's second law (\(F = ma\)) and kinematic concepts. The spring exerts equal force (\(F\)) on both carts. Cart A has mass \(m_A = 4\,\text{kg}\), Cart B has \(m_B = 8\,\text{kg}\). From \(a=\frac{F}{m}\), a smaller mass means a larger acceleration (\(a_A > a_B\)) since \(F\) is equal. With the same force - time interaction (impulse \(J = Ft\) is equal, so change in momentum \(mv\) is equal), and using kinematics (\(d=\frac{1}{2}at^2\) or \(d=\frac{v^2}{2a}\) with \(v=\frac{J}{m}\)), a larger acceleration (smaller mass) leads to greater distance. Cart A has less mass, so it accelerates more and travels farther. Volume is irrelevant here; the key is mass and acceleration.

Answer:

A. Cart A because it has the least mass