A rubber block is at rest on an inclined plane. When the angle of inclination of the plane is increased to 35.7°, the block begins to slide down the incline. Then, when the angle is decreased to 29.3°, the speed of the block is constant. What are the coefficients of static and kinetic friction between the block and the incline? static kinetic
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- A 2kg box is given a swift kick, and then allowed to slide along the ground until friction slows it to a stop. If the coefficient of static friction between this box and the ground is 0.7, and the coefficient of kinetic friction is 0.5, what is the magnitude of the acceleration that this box will experience? * 4.9 m/s/s 2.7 m/s/s 6.3 m/s/s 9.8 m/s/sGOAL 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.…A100-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.
- x Incorrect The force P is applied to the 30-kg block when it is at rest. Determine the magnitude and direction of the friction force exerted by the surface on the block if (a) P = 0, (b) P = 85 N, and (c) P = 131 N. (d) What value of P is required to initiate motion up the incline? The static and kinetic coefficients of friction between the block and the incline are us = 0.18 and µk = 0.12, respectively. The friction force is positive if up the incline, negative if down the incline. %3D P 30 kg 18° H, = 0.18 H = 0.12 12 Answers: (а) F 3D N (b) F (c) F = (d) P =A 40 N box is resting on a table when a 20 N force is applied to it horizontally. The coefficients of static and kinetic friction are 0.3 and 0.1, respectively. Which of the following best describes the resulting motion of the box? The motion of the box cannot be determined with the given information. The box accelerates in the direction of the applied force. The box remains at rest. The box moves with a constant velocity in the direction of the applied force.In the figure, two blocks are connected over a pulley. The mass of block A is 5.80 kg and the coefficient of kinetic friction between A and the incline is 0.360. Angle e of the incline is 31.0°. Block A slides down the incline at constant speed. What is the mass of block B? Frictionless, massless pulley B. Number i Units