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# Tension Tension, as its name indicates, is the force exerted by a rope, string, cable or similar object on one or more objects. Consider the case represented in the figure, where a block is attached to a rope. If a force $\overrightarrow{F}$ is applied to the rope, it will transmit this force...

# Tension Tension, as its name indicates, is the force exerted by a rope, string, cable or similar object on one or more objects. Consider the case represented in the figure, where a block is attached to a rope. If a force $\overrightarrow{F}$ is applied to the rope, it will transmit this force to the block. We say that the tension in the rope is equal to the magnitude of the force $\overrightarrow{F}$. * Tension is a pulling force * Tension has the direction of the rope * Tension is the same throughout the rope * Tension is a force, so it is measured in Newtons (N) **Example 1** Two blocks with masses $m_1 = 2 kg$ and $m_2 = 3 kg$ are connected by a rope. An external force $F = 10 N$ is applied to the block with mass $m_2$, as shown in the figure. Find the tension in the rope connecting the two blocks. **Solution** We can apply Newton's second law to each block separately. Let's start with the block of mass $m_1$: $T = m_1 a$ where $T$ is the tension in the rope and $a$ is the acceleration of the block. Now let's look at the block of mass $m_2$: $F - T = m_2 a$ where $F$ is the external force applied to the block. We now have two equations with two unknowns, $T$ and $a$. We can solve for $a$ in the first equation: $a = \frac{T}{m_1}$ and substitute into the second equation: $F - T = m_2 \frac{T}{m_1}$ Solving for $T$, we get: $T = \frac{m_1 F}{m_1 + m_2} = \frac{(2 kg)(10 N)}{2 kg + 3 kg} = 4 N$ Therefore, the tension in the rope connecting the two blocks is 4 N. **Example 2** A block of mass m = 5 kg is suspended from the ceiling by a rope. Find the tension in the rope. **Solution** The free body diagram is shown in the figure. The forces acting on the block are the weight $W = mg$ and the tension $T$ in the rope. Since the block is in equilibrium, the net force on the block must be zero: $T - W = 0$ Therefore, the tension in the rope is equal to the weight of the block: $T = W = mg = (5 kg)(9.8 m/s^2) = 49 N$ Therefore, the tension in the rope is 49 N.