a.) What is the smallest force parallel to the incline needed to keep the sofa from sliding down? b.) What parallel force is required to keep the sofa moving up the incline at a constant speed?c.) Assume the force, F, up the incline is 94N. What is the acceleration of the object?d.) From part c, how far will it move in 10s?
.) What is the smallest force parallel to the incline needed to keep the sofa from sliding down? The force that causes the sofa to accelerate as it slides down the incline is the component of its weight that is parallel to the incline. For the sofa, force parallel = 50 * sin 25 This is approximately 21.1 N Ff = 0.6 * 50 * cos 25 = 30 * cos 25 This is approximately 27.2 N Since the friction force is greater than the component of its weight that is parallel to the incline, the sofa will not slide. So no force is needed to prevent the sofa from sliding down the incline. b.) What parallel force is required to keep the sofa moving up the incline at a constant speed? This force is equal to the sum of those two forces. F = 50 * sin 25 + 30 * cos 25 This is approximately 48.32 N c.) Assume the force, F, up the incline is 94N. What is the acceleration of the object? The net force is equal to 94 N minus the sum of those two forces. Net force = 94 – (50 * sin 25 + 30 * cos 25) This is approximately 45.7 N Mass = 50/9.8 This is approximately 5.1 kg. a = [94 – (50 * sin 25 + 30 * cos 25)] ÷ (50/9.8) This is approximately 8.95 m/s^2. d.) From part c, how far will it move in 10s? Use the following equation. d = vi * t + ? * a * t^2, vi = 0 d = ? * [94 – (50 * sin 25 + 30 * cos 25)] ÷ (50/9.8) * 10^2 This is approximately 447.7 meters.
