91Ó°ÊÓ

Tension in a string is the force that is transmitted through the string when forces are applied on its ends. Imagine pulling a rope; the tension force is what holds the rope taut between you and the object. In our exercise, we have a light, inextensible string connecting two blocks with masses \(m\) and \(M\). When a horizontal force \(F\) is applied on block \(M\), tension develops in the string.Here, the tension \(T\) aims to keep the smaller block \(m\) moving together with the block \(M\). According to Newton's Second Law, the tension in the string can be calculated using the equation:\[ T = m \cdot a \]The tension is the cause of the smaller block \(m\) accelerating at the same rate as the whole system. By substituting the calculated acceleration \(a = \frac{F}{M + m}\), we find:\[ T = \frac{mF}{M + m} \]This formula tells us how the tension in the string depends on the masses of the two blocks and the external force applied.

Acceleration is the rate at which an object changes its velocity. In the context of this exercise, both blocks accelerate together because they are connected. Newton's Second Law gives the acceleration as the result of the net force divided by the total mass.First, consider the whole system of two blocks as a single object. The force \(F\) applied on block \(M\) is transferred through the string to block \(m\), causing the entire system to accelerate. Thus, the formula for acceleration is:\[ a = \frac{F}{M + m} \]This expression shows that the acceleration of the blocks is directly proportional to the external force \(F\) and inversely proportional to the combined mass of the blocks \(M + m\). It highlights the relationship between force, mass, and acceleration, encapsulating Newton's Second Law: \(F = ma\). With more mass, the system accelerates less for the same force, while with more force, acceleration increases.

Normal reaction is the force exerted by a surface perpendicular to an object resting upon it. It balances the gravitational force acting on the object, preventing it from falling through the surface.In our problem, both blocks are resting on a smooth horizontal ground, meaning there is no friction. For these blocks to remain in static equilibrium vertically, the normal reaction force needs to cancel out the weight of each block due to gravity.For block \(m\), the normal reaction force \(N_1\) can be described as:\[ N_1 = m \cdot g \]Here \(g\) is the acceleration due to gravity. Similarly, for block \(M\), its normal reaction force \(N_2\) is:\[ N_2 = M \cdot g \]These formulas illustrate how normal reaction forces ensure that the blocks do not move vertically, maintaining balance against the gravitational pull from the Earth. Each block's normal reaction is equal to its respective weight, demonstrating Newton's Third Law of motion where action and reaction forces are equal in magnitude and opposite in direction.