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# 1D Dynamics

A variety of phenomena can be captured by simplistic 1-dimensional models. Learn the essentials of mechanical motion in this stripped-down setting.

# Free Body Diagrams

The above diagram shows two blocks of respective masses $$m_1 = 7 \text{ kg}$$ and $$m_2 = 2 \text{ kg}$$ which are connected by a massless string and placed on a horizontal frictionless surface. If a force of $$F = 27 \text{ N}$$ is applied to $$m_1,$$ what is the force exerted by the string on $$m_2?$$

Two blocks of respective masses $$m_1 = 6 \text{ kg}$$ and $$m_2 = 3 \text{ kg}$$ are placed in contact on a horizontal frictionless surface. If a force of $$F = 27 \text{ N}$$ is applied to mass $$m_1,$$ what is the contact force on $$m_2?$$

A block of mass $$m = 15 \text{ kg}$$ is held stationary against a wall by applying a horizontal force $$F$$ on it, as shown in the above figure. If the coefficient of static friction between the wall and the block is $$\mu_s = 0.3$$ and the coefficient of kinetic friction is $$\mu_k = 0.2,$$ what is the minimum value of $$F$$ required to hold the block against the wall?

The gravitational acceleration is $$g = 10 \text{ m/s}^2.$$

Three blocks of respective masses $$m_1 = 9 \text{ kg}, m_2 = 5 \text{ kg} \text{ and } m_3 = 2 \text{ kg}$$ are placed in contact on a horizontal frictionless surface. If a force of $$F = 16 \text{ N}$$ is applied to $$m_1,$$ what is the contact force on $$m_2$$ (from $$m_1$$)?

A block of mass $$m = 5 \text{ kg}$$ is pulled by a force of $$F = 30\sqrt{2} \text{ N}$$ at an angle of $$\theta = 45^\circ$$ with the horizontal surface, as shown in the above figure. What is the acceleration of the block if the coefficient of kinetic friction between the surface and the block is $$\mu = 0.2,$$ assuming $$g = 10 \text{ m/s}^2?$$

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