Applying Newton's Laws — Question 2

Question 2

A table block and hanging mass have different force inventories

Take $g=10$ m/s$^2$. A 4 kg block lies on a frictionless horizontal table. A light cord runs from it over an ideal fixed edge pulley to a hanging 1 kg mass. The cord is taut.

1. Find their common acceleration magnitude and the tension.

2. Find the table’s normal force on the block.

3. If both start from rest, find the time for the hanging mass to descend 0.4 m.

Question 2 - Solution

A table block and hanging mass have different force inventories

(a) Couple the separate body equations.

$$T=4a,\quad10-T=a\ \Rightarrow\ \boxed{a=2\,\mathrm{m/s^2},\quad T=8\,\mathrm N}$$ The table block obeys $T=4a$. The hanging mass obeys $10-T=a$. Hence $a=2$ m/s$^2$ and $T=8$ N.

(b) Keep the table block’s vertical constraint.

$$\sum F_y=N-4g=0\ \Rightarrow\ N=40\,\mathrm N$$ The cord is horizontal at the block, so $N=4g=40$ N. This normal does not enter the horizontal acceleration equation.

(c) Use the available travel interval.

$$0.4=\tfrac12at^2\ \Rightarrow\ t=\sqrt{\frac{2(0.4)}2}=0.6325\,\mathrm s$$ $0.4=\tfrac12(2)t^2$, hence $t=\sqrt{0.4}\approx0.6325$ s, provided neither body hits a stop before that descent.