Question

3. A smaller 1-kg block is pushed horizontally against a larger 9-kg block by a force F, as shown below. The coefficient of static friction between the two blocks is 0.20, however the ground that the larger block sits on is frictionless. a. Draw a complete free-body diagram for each block. Hint: remember that the blocks exert forces on each other because they are in contact, and do not forget Newton's 3rd law. (10pts) b. What minimum force F is required so that as the blocks are pushed, the smaller block does not slide down against the larger block? Hint: use your free-body diagram and apply Newton's 2nd law (15pts) F=? 1-kg Ps =10.20 9-kg (the ground is frictionless) Extra credit for problem 3 (5pts): How would your answer to part b) change if there was friction along the ground? Explain. Again, I'm not looking for a numerical answer here but instead a conceptual explanation.

Answer 1

SOLUTION Part (a) Free body diagram for & kg block 'fs His For 9 kg block N N mg 7777 * Mg Mg weight of bigger N = mg = Weight of smaller block => 1x 9.8 = 9.8 N Normal force exerted by bigger block fs Friction force block 9x9.8 88.2 N by smaller M= 9 kg 4 ka N Normal force exerted block. N'- Normal force exerted by ground ma Part (b) Let the minimum force i acceleration of Bystem (beth block), a = Fmin Emin eo a = min Fmin m/s² M+m g+1 10 for block of 1 kg: Emin - N=ma = 1 x Fmin Emin . N Emin - Emin 9 min lo 1o

For given condition: - fs (fs max = mg = USN 4 м) us (9Fmin) i Emin 10mg I us 10 X 1 X 9.8 980.2 54• 4 4 N Fimin 54.4.4 N If there is friction along the ground:- acceleration, a = Fimin - Fa FR kinetic Saated friction en bigger block M + . for block of 1 kg! Emin - FR min - FR Emin -N = ma = Mim 1o → N = min Emin - FR g Emin & FR lo - mg = M N us [9Fm 9 Fimin + FR lo

.. long ls - 9 Fmin + Fr 1 g Emin long - FR lis ... . Emin lomg - FR ges meja Fmin = long gus FR Minimum fonce required decreases