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- The maximum lift force on a bat is proportional to the square of its flying speed v. For the hoary bat (Lasiurus cinereus), the magnitude of the lift force is given by Fl (0.018 N s2/m2) v2 The bat can fly in a horizontal circle by banking its wings at an angle , as shown in Figure P7.72. In this situation, the magnitude of the vertical component of the lift force must equal the bats weight. The horizontal component of the Figure P7.72. force provides the centripetal acceleration. (a) What is the minimum speed that the bat can have if its mass is 0.031 kg? (b) If the maximum speed of the bat is 10 m/s, what is the maximum banking angle that allows the bat to stay in a horizontal plane? (c) What is the radius of the circle of its flight when the bat flies at its maximum speed? (d) Can the bat turn with a smaller radius by flying more slowly?A car's bumper is designed to withstand a 4.0-km/h (1.1-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.A child of mass m swings in a swing supported by two chains, each of length R. If the tension in each chain at the lowest point is T, find (a) the childs speed at the lowest point and (b) the force exerted by the seat on the child at the lowest point. (Ignore the mass of the seat.)
- While jumping on a trampoline, sometimes you land on your back and other times on your feet. In which case can you reach a greater height and why?Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis, as in Figure P7.62. Molten metal is poured into the rotating cylinder and then cooled, forming the finished product. Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displaced toward the axis so that unwanted voids will not be present in the casting. Suppose a copper sleeve of inner radius 2.10 cm and outer radius 2.20 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be 100g. What rate of rotation is required? State the answer in revolutions per minute. Figure P7.62A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts (8.00105s). (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?
- Construct Your Own Problem Consider an astronaut in deep space cut free from her space ship and needing to get back to it. The astronaut has a few packages that she can throw away to move herself toward the ship. Construct a problem in which you calculate the time it takes her to get back by throwing all the packages at one time compared to throwing them one at a time. Among the things to be considered are the masses involved, the force she can exert on the packages through some distance, and the distance to the ship.A uniform pole is propped between the floor and the ceiling of a room. The height of the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling is 0.576. The coefficient of static friction between the pole and the floor is greater than that between the pole and the ceiling. What is the length of the longest pole that can be propped between the floor and the ceiling?If you lower the window on a car while moving, an empty plastic bag can sometimes fly out the window. Why does this happen?
- A soft tennis ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.10 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts (3.50103s). (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?In Chapter 5 we will define the center of mass of an object The center of mass moves with constant acceleration when constant forces act on the object A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground. How high above this point is her center of mass (a) 0.100 s, (b) 0.200 s, (c) 0.300 s, and (d) 0.500 s thereafter?You have been hired as an expert witness in the case of a factory owner suing a demolition company. The particular case involves a smokestack at a factory being demolished. In order to save money, the factory owner wanted to move the smokestack to a nearby factory that was being built. The demolition company guaranteed to deliver the undamaged smokestack to the new factory by toppling the smokestack freely onto a huge cushioned platform lying on the ground. The then-horizontal smokestack would have been loaded onto a long truck rig for transport to the new factory. However, as the smokestack toppled, it broke apart at a point along its length. The factory owner is blaming the demolition company for the destruction of his smokestack. The demolition company is claiming that there was a defect in the smokestack and that is the reason for its destruction. What advice do you give the attorney who is handling the case on the side of the factory owner?