EXERC ISE 4.12 The ramp in Example 412 is roughed up and the experiment repeated. (a)What is the new coefficient of static friction if the maximum angle turns out to be 30.0^circ (b) Find the maximum static friction force that acts on the block. ANSWER (a) 0.577 (b) 12 gN

(a) The new coefficient of static friction is 0.577.(b) The maximum static friction force that acts on the block is 112.9 N.

## Step 1The problem involves the concept of static friction and its coefficient. The coefficient of static friction is the ratio of the force of static friction between two bodies and the force pressing them together. In this case, the force pressing the bodies together is the weight of the block.## Step 2The coefficient of static friction can be calculated using the formula:### \( \mu = \tan(\theta) \)where is the angle of the ramp. ## Step 3Substituting the given angle of into the formula, we get:### \( \mu = \tan(30.0^{\circ}) = 0.577 \)## Step 4The maximum static friction force that acts on the block can be calculated using the formula:### where is the normal force. In this case, the normal force is equal to the weight of the block, which is .## Step 5Substituting the values into the formula, we get:###