Incline Planes with Free Body Diagrams 1. A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end as shown below. Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30.0 N. (b) 60.0 N, and (c) 90.0 N. 3 pts 2. A person pushes a 14.0-kg lawn mower at constant speed with a force of F = 88.0N directed along the handle. which is at an angle of 45.0 to the horizontal, as shown below. (0) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then (c) the normal force exerted vertically upward on the mower by the ground. (0') What force must the person exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds. assuming the same friction force? 6 pts 3. A 15.0-kg box is released on a 32 incline and accelerates down the incline at 0.30 m/s2 . Find the friction force impeding its motion. What is the coefcient of kinetic friction? 4 pts 4. (a) A box sits at rest on a rough 30 inclined plane. Draw the free-body diagram, showing all the forces acting on the box. (b) How would the diagram change if the box were sliding down the plane? (c) How would it change if the box were sliding up the plane after an initial shove? 6 pts 5. A 75.0-kg person stands on a scale in an elevator. What does the scale read (in N and in kg) when the elevator is (a) at rest, (b) ascending at a constant speed of 3.0m/s (c) falling at 3.0m/s (d) accelerating upward at 3.0m/s', (e) accelerating downward at 3.0m/s?? 5 pts 6. If the coefficient of kinetic friction between a 35-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if u is zero? 4 pts 7. A force of 48.0 N is required to start a 5.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 48.0-N force continues, the box accelerates at 0.70 m/s . What is the coefficient of kinetic friction? 4 pts8. A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 m/s? 4 pts