The coefficient of static friction at all contacting surfaces is μ. The blocks are identical and weigh W. Determine the angle at which the blocks begin to slide. A B 0
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- GOAL Apply the concept of static friction to an object resting on an incline. PROBLEM Suppose a block with a mass of 2.50 kg is resting on a ramp. If the coefficient of static friction between the block and ramp is ng sin e 0.350, what maximum angle can the ramp make with the horizontal mg cos e e before the block starts to slip down? STRATEGY This is an application of Newton's second law involving an object in equilibrium. Choose tilted coordinates, as in the figure. Use the fact that the block is just about to slip when the force of static friction takes its maximum value, f. = 4n. SOLUTION Write Newton's laws for a static system (1) EF = mg sin e - u̟n = 0 in component form. The gravity force (2) EF = n - mg cos e = 0 has two components. Rearrange Equation (2) to get an n = mg cos 8 expression for the normal force n. Substitute the expression for n into EF, = mg sin 8 - H mgcos 0 = 0 → tan 8 =u. Equation (1) and solve for tan 0. Apply the inverse tangent function to get the answer.…Choose the coefficient of friction wisely. Relevant information is given in the textbook. a. What is the maximum frictional force in the knee joint of a person who supports 70.0 kg of her mass on that knee? Fmax 686.7 XN b. During strenuous exercise it is possible to exert forces to the joints that are easily ten times greater than the weight being supported. What is the maximum force of friction under such conditions? (The frictional forces in joints are relatively small in all circumstances except when the joints deteriorate, such as from injury or arthritis. Increased frictional forces can cause further damage and pain.) Fmax = NA100-kg sofa needs to be moved across a level floor. The coefficient of static friction between the sofa and the floor is 0.40. Two physics students decide to apply a force F!" on the sofa. One student recommends that the force be applied upward at an angle theta above the horizontal. The other student recommends that the force be applied downward at an angle theta below the horizontal. Explain which student has the better idea and why.
- 4. A block of mass 3.00-kg is pushed against a wall by a force P that makes an angle of 50.0° with the horizontal as shown in the figure below. The coefficient of static friction between the block and the wall is 0.250. a. Determine the possible values for the magnitude of P that allow the block to remain stationary. PCalculate the ratio of the drag force on a jet flying at 885 km/h at an altitude of 8.6 km to the drag force on a prop-driven transport flying at half that speed and altitude. The density of air is 0.46 kg/m³ at 8.6 km and 0.71 kg/m³ at 4.3 km. Assume that the airplanes have the same effective cross-sectional area and drag coefficient C. Number i UnitsA 9.61kg box on a ramp with an incline of 26.36° slips, giving it an acceleration of 0.31m/s2. What is the coefficient of kinetic friction between the box and the ramp?