(a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 24.5° with the horizontal. A 30.0-kg piece of luggage is placed on the carousel, 7.46 m from the axis of rotation. The travel bag goes around once in 37.5 s. Calculate the magnitude of the force of static friction between the bag and the carousel. N (b) The drive motor is shifted to turn the carousel at a higher constant rate of rotation, and the piece of luggage is bumped to a position 7.94 m from the axis of rotation. The bag is on the verge of slipping as it goes around once every 30.5 s. Calculate the coefficient of static friction between the bag and the carousel.

If centripetal force is directed toward the center, why do you feel that you are ‘thrown’ away from the center as a car goes around a curve? Explain.

A bag of cement weighing 325 N hangs in equilibrium from three wires as suggested in Figure P4.23. Two of the wires make angles 1 = 60.0 and 2 = 40.0 with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires. Figure P4.23 Problems 23 and 24.

An office door is given a sharp push and swings open against a pneumatic device that slows the door down and then reverses its motion. At the moment the door is open the widest, (a) does the doorknob have a centripetal acceleration? (b) Does it have a tangential acceleration?

If you were to stop a spinning wheel with a constant force, where on the wheel would you apply the force to produce the maximum negative acceleration?

In a television commercial, a small, spherical bead of mass 4.00 g is released from rest at t=0in a bottle of liquid shampoo. The terminal speed is observed to be 2.00 cm/s. Find (a) the value of the constant bin the equation v=mgb(1ebt/m), and (b) the value of the resistive force when the bead reaches terminal speed.

Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen below. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force) and the vertical normal force (which must equal the system’s weight). (a) Show that (as defined as shown) is related to the speed vand radius of curvature rof the turn in the same way as for an ideally banked roadway—that is, =tan1(v2/rg) . (b) Calculate for a 12.0-m/s turn of radius 30.0 m (as in a race).

A 75.0-g arrow, fired at a speed of 110 m/s to the left, impacts a tree, which it penetrates to a depth of 12.5 cm before coming to a stop. Assuming the force of friction exerted by the tree is constant, what are the magnitude and direction of the friction force acting on the arrow?

We know from studying friction forces that static friction increases with increasing normal force between the surfaces, which becomes important for vehicles traveling on icy or snowy roads that have coefficients of static friction much smaller than those of dry pavement. In particular, the greater the normal force on the drive wheels (those coupled to the engine), the better the traction. The horizontal position of the center of mass of a typical compact automobile is located 1.1 m toward the rear as measured from the front wheel axle. The wheelbase (distance from the front wheel axle to the rear wheel axle) is 2.7 m. Assume the car is stationary on level ground and has a weight of 12,000 N. Determine the total normal force on the two front tires and on the two rear tires. Which do you suppose are the drive wheels in this case?

A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of 3.00im/s at one instant. Eight seconds later, its velocity is (8i+10j)m/s. Assuming the rocket engine exerts a constant horizontal force, find (a) the components of the force and (b) its magnitude.