Answer to Question #156458 in Classical Mechanics for Flockshot

Question

As shown in the figure below, two forces are applied horizontally to two blocks in contact. The horizontal surface on which the blocks slide frictionless. if F = 6.0N and M=1.0kg, what is the magnitude of the force exerted on the large block of mass 3M by the small block of mass 2M.

https://i.gyazo.com/25f5ef792c93e6b6a36a11cfb984d5a5.png

Answer 1

Let's first find the acceleration of the system of two blocks from the Newton's Second Law of Motion:

$$2F-F=(3M+2M)a,$$ $$a=\dfrac{F}{5M}=\dfrac{6.0\ N}{5\cdot1.0\ kg}=1.2\ \dfrac{m}{s^2}.$$

Then, we can find the net force on the first block with mass $3M$:

$$F_{1,net}=3Ma=3\cdot1.0\ kg\cdot1.2\ \dfrac{m}{s^2}=3.6\ N.$$

Finally, we can find the magnitude of the force exerted on the large block of mass 3M by the small block of mass 2M:

$$2F-F_{21}=F_{1,net},$$ $$F_{21}=2F-F_{1net}=2\cdot6.0\ N-3.6\ N=8.4\ N.$$

Answer:

$F_{21}=8.4\ N.$