Question

1. four different boxes are being pushed with an equal amount of force. the mass of each box is listed below.

which of the following statements accurately describe the acceleration of each box?
select two correct answers.
box a would have a greater acceleration than box b but less acceleration than box d.
box c would have a greater acceleration than box b but less acceleration than box d.
box b would have the greatest acceleration and box d would have the least acceleration.
box a would have a greater acceleration than box b but less acceleration than box d.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Rearranging for acceleration gives \(a=\frac{F}{m}\). Since the force \(F\) is the same for all boxes, \(a\propto\frac{1}{m}\) (inversely proportional to mass).

Step2: Compare accelerations based on mass

• For Box A (\(m = 12\space kg\)), Box B (\(m = 6\space kg\)), Box C (\(m = 10\space kg\)), Box D (\(m = 22\space kg\))
• Using \(a=\frac{F}{m}\), when \(F\) is constant:
• If \(m_A=12\space kg\) and \(m_D = 22\space kg\), since \(12<22\), then \(a_A=\frac{F}{12}\) and \(a_D=\frac{F}{22}\), so \(a_A > a_D\) (Box A has greater acceleration than Box D).
• If \(m_C = 10\space kg\) and \(m_D=22\space kg\), since \(10 < 22\), then \(a_C=\frac{F}{10}\) and \(a_D=\frac{F}{22}\), so \(a_C > a_D\) (Box C has greater acceleration than Box D)

Answer:

Box C would have a greater acceleration than Box D. Box A would have a greater acceleration than Box D.