A red trolley of mass 9.7 kg and a blue trolley of mass 2.2 kg with frictionless wheels is pushed by a force of 11.7 N to the right. What is the reaction force of the red trolley acting on the blue trolley?

Question

BlackTom AI · Accepted Answer

Newton’s second law: the whole pair accelerates with a = F_external / (m_red + m_blue). The contact force between them is what accelerates the red trolley, so its magnitude equals m_red · a and acts backward on the blue trolley (reaction).

1) Relevant concepts
- Newton’s 2nd law: F_net = m a.
- For two touching bodies on a frictionless surface, the external push accelerates the combined mass; the contact force between them transmits acceleration to the trailing trolley. Action–reaction pair: blue pushes red forward, red pushes blue backward with equal magnitude.

2) Step-by-step reasoning
- Total mass = m_red + m_blue = 9.7 kg + 2.2 kg = 11.9 kg.
- Acceleration of the system: a = F_external / (total mass) = 11.7 N / 11.9 kg.

3) Calculations (intermediate steps)
- a = 11.7 / 11.9 = 0.983193277... m/s^2 (≈ 0.9832 m/s^2).
- Contact force exerted by the blue on the red (forward on red) = m_red · a = 9.7 kg × 0.9831933 m/s^2 = 9.5369 N.
- By Newton’s third law the red trolley exerts an equal and opposite reaction on the blue: 9.5369 N (≈ 9.54 N) directed backward on the blue.

4) Why this is correct
The red trolley’s forward acceleration must come from the contact push of the blue trolley; that contact force equals m_red·a. Equivalently, from the blue’s free-body: 11.7 N (hand) − F_red_on_blue = m_blue·a → F_red_on_blue = 11.7 − 2.2·a = 11.7 − 2.163 ≈ 9.537 N, same result.

5) Why the other choices are incorrect
- b (2.65 N) and c (2.16 N): these are close to m_blue·a (≈2.16 N) or other miscomputed values, not the contact reaction from the red trolley. c = 2.16 N is the net acceleration term m_blue·a, not the reaction force from the heavier red trolley. 
- d (51.59 N) is far too large compared to the applied 11.7 N and the masses; it is not physically consistent.

6) Conclusion
The reaction force of the red trolley acting on the blue trolley is approximately 9.54 N, matching answer a.

A red trolley of mass 9.7 kg and a blue trolley of mass 2.2 kg with frictionless wheels is pushed by a force of 11.7 N to the right. What is the reaction force of the red trolley acting on the blue trolley?单项选择题

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