Newton's Third Law — Question 5

Question 5

Contact forces remain paired during a collision

During a short collision, a 1000 kg cart exerts a 6000 N force east on a 1500 kg cart. Consider only the horizontal acceleration due to this mutual interaction at that instant.

1. Find the reaction force.

2. Find each interaction-induced acceleration.

3. Can unequal deformation imply unequal third-law forces?

Question 5 - Solution

Contact forces remain paired during a collision

(a) Apply the pair relation at the same instant.

$$\boxed{F_{1500\to1000}=-F_{1000\to1500}=-6000\,\mathrm N}$$ The 1500 kg cart exerts 6000 N west on the 1000 kg cart.

(b) Use each inertial mass.

$$a_{1000}=-6000/1000=-6,\quad a_{1500}=6000/1500=4\quad\mathrm{m/s^2}$$ The accelerations due to this interaction are -6 m/s$^2$ for the 1000 kg cart and +4 m/s$^2$ for the 1500 kg cart.

(c) Do not infer force inequality from different responses.

$$m_Aa_A+m_Ba_B=1000(-6)+1500(4)=0\,\mathrm N$$ Deformation depends on material properties and structure as well as force; acceleration depends on mass. Different visible outcomes do not alter the equality of the mutual contact forces. Other external forces, if present, affect each net force separately.