The next two questions pertain to the situation described below. A block of mass

Question

The next two questions pertain to the situation described below. A block of mass M-3 kg is placed on an inclined plane with an angle -36 degrees. A string anchored near the top of the ramp is attached to the block in order to prevent the block from sliding down the ramp (Without the string, static friction alone would be insufficient to keep the block from slipping.) The coefficient of static friction is us -0.08 and the tension in the string is T. 9) Which is the correct free body diagram of the forces on the block when it is at rest? HsN SN HsN mg mg mg a. A (left diagram) b. C (right diagram) c. B (center diagram) 10) What is the minimum tension in the string needed to hold the block in place? a. 15.38 N b. 5.13 N c. 19.18 N d. 22.4 N e. 25.17 N

Explanation / Answer

Normal is along normal to the surface, Tension and friction forces are up the incline, and gravity is vertically downwards. So, The correct free body diagram of the forces on the block when it is at rest is b. C(right diagram).

With the given values, the minimum tension in the needed to hold teh block in place can be found by the equilibrium. So, Along vertical, Ncos36+0.08Nsin36+Tsin36= Mg= 29.43

Along Horizontal, Tcos36+ 0.08Ncos36= Nsin36; Or, Tcos36= N(sin36-0.08cos36); Or, T= 0.6465N

So, N(cos36+0.08sin36+0.6465sin36)= 29.43; So, N= 23.81

So, T= 23.81*0.6465= 15.38N.

So, (a) T= 15.38N

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