A block with mass \( m=2.02 \mathrm{~kg} \) sits on top of a block with mass \( M=5.72 \mathrm{~kg} \) that is placed on a table. The coefficients of kinetic friction between \( m \) and \( M \) is \( \mu_{k 1}=0.24 \) and the coefficient of kinetic friction between \( M \) and table is \( \mu_{k 2}=0.192 \). A string with negligible mass is connected to each mass and wraps halfway around a pulley with negligible mass, as shown in the figure. What is the acceleration of block \( M \) in the units \( \mathrm{m} / \mathrm{s}^{2} \) at the instant \( 46.031 \mathrm{~N} \) force is applied on it horizontally to the left as shown in the figure? \( g=9.8 \mathrm{~m} / \mathrm{s}^{2} \) Answer:
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First, we need to find the gravitational force acting on both blocks. This can be calculated using the formula: F_gravity = m * g For block m: F_gravity_m = 2.02 kg * 9.8 m/s² = 19.796 N For block M: F_gravity_M = 5.72 kg * 9.8 m/s² = 56.056 N Show more…
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A block $A$ of mass $m_{\mathrm{i}}$ rests on a horizontal table. $\mathrm{A}$ light string connected to it passes over a friction less pulley at the edge of table and from its other end another block $B$ of mass $m_{2}$ is suspended. The coefficient of kinetic friction between the block and the table is $\mu_{k} .$ When the block $A$ is sliding on the table, the tension in the string is (a) $m_{1} m_{2}\left(1+\mu_{k}\right) g /\left(m_{1}+m_{2}\right)$ (b) $\quad m_{1} m_{2}\left(1-\mu_{k}\right) \mathrm{g} /\left(m_{1}+m_{2}\right)$ (c) $\left(m_{2}+\mu_{k} m_{1}\right) \mathrm{g} /\left(m_{1}+m_{2}\right)$ (d) $\left(m_{2}-\mu_{k} m_{1}\right) g /\left(m_{1}+m_{2}\right)$
LAW OF MOTION
Laws of Motion
A block of mass $M$ rests on a block of mass $\mathrm{M} 1=5.00 \mathrm{~kg} M_{1}=5.00 \mathrm{~kg}$ which is on a tabletop (Figure 5-31). A light string passes over a massless, frictionless pulley and connects the blocks. The coefficient of kinetic friction $\mu_{\mathrm{k}}$ at both surfaces equals $0.330 .$ A force of magnitude $60.0 \mathrm{~N}$ pulls the upper block to the left and the lower block to the right. The blocks are moving at a constant speed. Determine the mass of the upper block. Example $5-4$
A block of mass $m_{1}=2.00 \mathrm{kg}$ and a block of mass $m_{2}=$ 6.00 $\mathrm{kg}$ are connected by a massless string over a pulley in the shape of a solid disk having radius $R=0.250 \mathrm{m}$ and mass $M=10.0 \mathrm{kg}$ . These blocks are allowed to move on a fixed wedge of angle $\theta=30.0^{\circ}$ as shown in Figure $\mathrm{P} 10.37$ . The coefficient of kinetic friction is 0.360 for both blocks. Draw free-body diagrams of both blocks and of the pulley. Determine (a) the acceleration of the two blocks and (b) the tensions in the string on both sides of the pulley.
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