Applying Newton's Laws — Question 5

Question 5

Contact can transmit a push but cannot keep blocks together under a pull

Blocks A and B of masses 2 and 3 kg touch on a frictionless line, A left of B. Initially at rest, A is pushed right with 10 N. In a separate trial A is pulled left with 10 N; there is no connector.

1. Find acceleration and contact force in the push trial.

2. Test a common-acceleration assumption in the pull trial.

3. Give the actual accelerations immediately after the pull begins.

Question 5 - Solution

Contact can transmit a push but cannot keep blocks together under a pull

(a) Use the joined motion while contact is compressive.

$$10=(2+3)a\ \Rightarrow\ \boxed{a=2\,\mathrm{m/s^2},\quad C=3a=6\,\mathrm N}$$ The common acceleration is $10/5=2$ m/s$^2$. The force on B is $3(2)=6$ N rightward, supplied by A’s push.

(b) Check whether contact would have to pull.

$$a_{\mathrm{assumed}}=-10/5=-2,\quad C_{\mathrm{required}}=3(-2)=-6\,\mathrm N<0$$ Common acceleration would be -2 m/s$^2$, requiring -6 N on B from A. Ordinary side contact cannot pull B left, so this constraint is inadmissible.

(c) Release the failed contact.

$$C=0:\quad a_A=-10/2=-5\,\mathrm{m/s^2},\quad a_B=0$$ The blocks separate. A accelerates at $-10/2=-5$ m/s$^2$, B at zero, and contact force is zero. The common-acceleration model works only while a compressive contact exists.