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

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 \( m_2? \)

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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 \( m_2?\)

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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 \( g = 10 \text{ m/s}^2. \)

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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 \(m_1\))?

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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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