6 - Circular Motion and Other Applications of Newton's Laws

A radial line at 350 north latitude assume that the

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Unformatted text preview: nt b ? (b) What is the acceleration at t 0? (c) What is the acceleration when the speed is 0.150 m/s? 32. (a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm3) falling through the air if its radius is 8.00 cm. (b) From what height would a freely falling object reach this speed in the absence of air resistance? 33. Calculate the force required to pull a copper ball of radius 2.00 cm upward through a fluid at the constant speed 9.00 cm/s. Take the drag force to be proportional to the speed, with proportionality constant 0.950 kg/s. Ignore the buoyant force. 34. A fire helicopter carries a 620-kg bucket at the end of a cable 20.0 m long as in Figure P6.34. As the helicopter flies to a fire at a constant speed of 40.0 m/s, the cable makes an angle of 40.0° with respect to the vertical. The bucket presents a cross-sectional area of 3.80 m2 in a plane perpendicular to the air moving past it. Determine the drag coefficient assuming that the resistive WEB 37. 38. 39. force is proportional to the square of the bucket’s speed. A small, spherical bead of mass 3.00 g is released from rest at t 0 in a bottle of liquid shampoo. The terminal speed is observed to be vt 2.00 cm/s. Find (a) the value of the constant b in Equation 6.4, (b) the time the bead takes to reach 0.632vt , and (c) the value of the resistive force when the bead reaches terminal speed. The mass of a sports car is 1 200 kg. The shape of the car is such that the aerodynamic drag coefficient is 0.250 and the frontal area is 2.20 m2. Neglecting all other sources of friction, calculate the initial acceleration of the car if, after traveling at 100 km/h, it is shifted into neutral and is allowed to coast. A motorboat cuts its engine when its speed is 10.0 m/s and coasts to rest. The equation governing the motion of the motorboat during this period is v vi e ct, where v is the speed at time t, vi is the initial speed, and c is a constant. At t 20.0 s, the speed is 5.00 m/s. (a) Find the constant c. (b) What is the speed at t 40.0 s? (c) Differentiate the expression for v (t ) and thus show that the acceleration of the boat is proportional to the speed at any time. Assume that the resistive force acting on a speed skater is f kmv 2, where k is a constant and m is the skater ’s mass. The skater crosses the finish line of a straight-line race with speed vf and then slows down by coasting on his skates. Show that the skater ’s speed at any time t after crossing the finish line is v (t ) vf /(1 ktvf ). You can feel a force of air drag on your hand if you stretch your arm out of the open window of a speeding car. (Note: Do not get hurt.) What is the order of magnitude of this force? In your solution, state the quantities you measure or estimate and their values. (Optional) 6.5 Numerical Modeling in Particle Dynamics 40. A 3.00-g leaf is dropped from a height of 2.00 m above the ground. Assume the net downward force exerted on the leaf is F mg bv, where the drag factor is b 0...
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