Newton’s Laws 1. A block is given an initial velocity of 4.00 m/s up a frictionless 21.0° incline. How far up the incline does the block slide before coming (momentarily) to rest? 2. .37 g samara -- the winged fruit of a maple tree -- falls toward the ground with a constant speed of 0.9 m/s (Figure 5-29). (a) What is the force of air resistance exerted on the samara? (b) If the constant speed of descent is greater than 0.9 m/s, is the force of air resistance greater than, less than, or the same as in part (a)? 3. A gardener mows a lawn with an old-fashioned push mower. The handle of the mower makes an angle of 32° with the surface of the lawn. (a) If a 204 N force is applied along the handle of the 18 kg mower, what is the normal force exerted by the lawn on the mower? (b) If the angle between the surface of the lawn and the handle of the mower is decreased, does the normal force exerted by the lawn increase, decrease, or stay the same? 4. Seatbelts provide two main advantages in a car accident: (i) they keep you from being thrown from the car, and (ii) they reduce the force that acts on you during the collision to survivable levels. The second benefit can be illustrated by comparing the net force exerted on the driver of a car in a head-on collision with and without a seatbelt. (a) A driver wearing a seatbelt decelerates at the same rate as the car itself. Since modern cars have a "crumple zone" built into the front of the car, the car will decelerate over a distance of roughly 1.0 m. Find the net force acting on a 52 kg driver who is decelerated from 20 m/s to rest in a distance of 1.0 m. (b) A driver who does not wear a seatbelt continues to move forward with a speed of 20 m/s (due to inertia) until something solid is encountered. The driver now comes to rest in a much shorter distance -- perhaps only a centimeter. Find the net force acting on a 52 kg driver who is decelerated from 20 m/s to rest in 1.0 cm. 5. Two blocks are connected by a string, as shown in Figure 6-28. The smooth inclined surface makes an angle of = 43° with the horizontal, and the block on the incline has a mass m1 = 5.5 kg. Find the mass m2 of the hanging block that will cause the system to be in equilibrium. 6. A m1 = 4.00 kg block on a smooth tabletop is attached by a string to a hanging block of mass m2 = 2.00 kg, as shown in Figure 6-34. The blocks are released from rest and allowed to move freely. (a) Is the tension in the string greater than, less than, or equal to the weight of the hanging mass? (c) Find the tension in the string. 6. Referring to the Interactive Figure (a dump truck with a bed that tilts until a box rested there starts to slip), suppose the coefficients of static and kinetic friction between the crate and the truck bed are 0.407 and 0.326, respectively. (a) Determine the angle at which the crate begins to slide. (c) Find the length of time it takes for the crate to slide a distance of 2.75 m when the tilt angle has the value found in part (b). Now, use what you have learned to answer the following. Suppose the coefficients of static and kinetic friction between the crate and the truck bed are 0.847 and 0.678, respectively. (d) Does the crate begin to slide at a tilt angle that is greater than, less than, or equal to 35.1°? (e) Verify your answer to part (d) by determining the angle at which the crate begins to slide. (f) Find the length of time it takes for the crate to slide a distance of 2.75 m when the tilt angle has the value found in part (e). 7. Two drivers traveling side-by-side at the same speed suddenly see a deer in the road ahead of them and begin braking. Driver 1 stops by locking up his brakes and screeching to a halt; driver 2 stops by applying her brakes just to the verge of locking, so that the wheels continue to turn until her car comes to a complete stop. All other factors being equal, is the stopping distance of driver 1 greater than, less than, or equal to the stopping distance of driver 2? 8. When you push a 2.10 kg book resting on a tabletop it takes 1.80 N to start the book sliding. Once it is sliding, however, it takes only 1.50 N to keep the book moving with constant speed. What are the coefficients of static and kinetic friction between the book and the tabletop? 9. To move a large crate across a rough floor, you push on it with a force F at an angle of 21° below the horizontal, as shown in Figure 6-21. Find the force necessary to start the crate moving, given that the mass of the crate is m = 35 kg and the coefficient of static friction between the crate and the floor is 0.48. 10. To move a large crate across a rough floor, you push on it with a force F at an angle of 21°, below the horizontal, as shown in Figure 6-21 (same figure as above). Find the acceleration of the crate, given that the mass of the crate is m = 31 kg, the applied force is 319 N and the coefficient of kinetic friction between the crate and the floor is 0.59. 11. A 13 kg crate is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to 22.8° the crate begins to slide downward. (a) What is the coefficient of static friction between the crate and the ramp? (b) At what angle does the crate begin to slide if its mass is doubled? 12. A force of 25.0 N is required to start a 3.1 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 25.0 N force continues, the box accelerates at 0.50 m/s2. What is the coefficient of kinetic friction? 13. A box sits at rest on a rough 30° inclined plane. Draw the free-body diagram, showing all the forces acting on the box. (Do this on paper. Your instructor may ask you to turn in this work.) (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? 14. Two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface (see figure). A 650 N force is exerted on the 65 kg crate. The coefficient of kinetic friction is 0.24. (a) Calculate the acceleration of the system. (b) Calculate the force that each crate exerts on the other (c) With the crates reversed, calculate the force that each crate exerts on the other. 15. Your 3.30 kg physics book is next to you on the horizontal seat of your car. The coefficient of static friction between the book and the seat is 0.610, and the coefficient of kinetic friction is 0.510. Suppose you are traveling at 54.0 km/h = 15.0 m/s and brake at a constant rate to a stop over a distance of 36.8 m. (a) Will the book start to slide over the seat? (b) What force does the seat exert on the book in this process?