A 10 kg block is placed on a smooth (frictionless) ramp inclined at $30^\circ$ to the horizontal. Calculate the acceleration of the block down the ramp. ($g = 9.8 \text{ m/s}^2$)

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A 5 kg wooden crate is on a $25^\circ$ ramp. The coefficient of kinetic friction is $\mu_k = 0.2$. If it starts sliding from rest, what is its acceleration? ($g = 9.8 \text{ m/s}^2$)

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A 20 kg block is on a $40^\circ$ incline with $\mu_k = 0.3$. A person pushes it up the incline with a horizontal force $P = 300 \text{ N}$. Find the block's acceleration up the ramp. ($g = 9.8 \text{ m/s}^2$)

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A 1000 kg elevator is being pulled upward by a cable. If the tension in the cable is 12,000 N, what is the upward acceleration of the elevator? (Assume $g = 9.8 \text{ m/s}^2$)

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Block A ($m_A = 4 \text{ kg}$) and Block B ($m_B = 6 \text{ kg}$) are connected by a massless string on a frictionless horizontal table. A horizontal force $F = 30 \text{ N}$ pulls on Block B. Find the acceleration of the system and the tension in the connecting string.

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An Atwood machine consists of two masses, $m_1 = 3 \text{ kg}$ and $m_2 = 5 \text{ kg}$, connected by a massless string over a frictionless pulley. Find the acceleration of the masses and the tension in the string. ($g = 9.8 \text{ m/s}^2$)

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A 50 kg box rests on a horizontal floor. A worker applies a horizontal pushing force of 200 N. The coefficient of kinetic friction between the box and the floor is $\mu_k = 0.3$. Determine the acceleration of the box. ($g = 9.8 \text{ m/s}^2$)

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A 40 kg crate sits on a floor. The coefficient of static friction is $\mu_s = 0.6$ and kinetic friction is $\mu_k = 0.4$. A person pushes with $200 \text{ N}$ of horizontal force. Does the crate move? If not, what is the force of static friction?

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A 25 kg lawnmower is pushed with a force of $150 \text{ N}$ directed at a downward angle of $30^\circ$ relative to the horizontal. If $\mu_k = 0.2$, what is its acceleration?

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