3. Two identical blocks (Block 1 and Block 2) have a mass of 30 kg each and have been manufactured with a top surface slope of 25°. By flipping Block 1 upside-down the two blocks can sit one-on-top- of-the-other as shown below. This problem has 2 scenarios: (a) For Scenario A, draw the complete free body diagram of Block 2 and establish the smallest value of $\mu_{12}$, the coefficient of friction for the surface between Block 1 and Block 2, so that Block 1 does not slide on Block 2. (b) For Scenario B, assume that $\mu_{12} = 0.5$ and that that coefficient of friction between Block 2 and the ground, $\mu_{2G} = 0.4$. Determine the smallest value of T to make Block 2 slide. Scenario A Scenario B Block 1 Block 1 25° Block 2 T Block 2
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Problem 14: Two blocks sliding Two blocks are arranged one on top of each other on a table, as shown in Fig: 2.33. The coefficient of kinetic friction between the blocks is μk. Provided the two blocks are in relative motion, the magnitude of the frictional force that each block exerts on the other is μkN, where N is the normal force that each block exerts on the other. There is no friction between the lower block (mass m2) and the table. A known force is applied to the upper block (mass m) which causes both blocks to accelerate. The goal of this problem is to find the blocks' acceleration, namely a1 for the upper block and a2 (a2 < a1) for the lower block, as shown in the figure, in terms of known quantities: F, m1, m2, g, and μk. Sketch force diagrams, one for each block, indicating all relevant forces. Write down Newton's second law for each mass. What are the blocks' accelerations in the vertical direction? Give both vertical accelerations. Using your answers to (b) and (c), determine a1 and a2?
Keerti J.
Two blocks rest on a horizontal frictionless surface as shown. The surface between the top and bottom blocks has static friction sufficient for there to be no slipping between the two blocks. A force of 60 N is applied to the bottom block, as suggested in the figure. The top block has a mass of 5 kg, while the bottom block has a mass of 10 kg. What is the acceleration of the two-block system? What is the force of static friction between the top and bottom blocks? What is the minimum coefficient of static friction on the bottom block?
Sahil K.
Threc blocks $A, B$ and $C$ of equal mass $m$ are paced one over the other on a smooth horizontal ground as in the figure. Cocflicicnt of friction bclween any two blocks of $A, B$ and $C$ is $1 / 2$. Find the maximum valuc of mass of block $D$ so that the blocks $A, B$ and $C$ move withoul slipping over cach other. Solution Blocks $A$ and $C$ both move due to friction. But less friction is available to $A$ compared with $C$ because normal reaction between $A$ and $B$ is less. Maximum friction between $A$ and $B$ can be $f_{\max }=\mu m_{A} g=(1 / 2) m g$ Maximum accelcration of $A$ can be $a_{\max }-\frac{f_{\text {naax }}}{m}-\frac{g}{2}$ Further $a_{\max }-\frac{m_{D} g}{3 m \mid m_{D}} \Rightarrow \frac{g}{2}-\frac{m_{D} g}{3 m \mid m_{D}} \quad m_{D}-3 m$
Laws of Motion and Friction
Section A
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