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physics
mechanics

Questions and Answers of Mechanics

Coefficient of Friction A clean brass washer slides along a horizontal clean steel surface until it stops. Using the values from Table 5.1, how many times farther would it slide with the same initial
Consider the system shown in Fig. 5.54. Block A weighs 45.0 N and block B weighs 25.0 N. Once block B is set into downward motion, it descends at a constant speed.(a) Calculate the coefficient of
Two crates collected by a rope lie on a horizontal surface (Fig. 5.55). Crate A bas mass mA and crate B bas mass mB' the coefficient of kinetic friction between each crate and the surface is μt.
Rolling Friction two bicycle tires are set rolling with the same initial speed of 3.50 m/s on a long, straight road, and the distance each travels before its speed is reduced by half is measured. One
Wheels you find that it take a horizontal force of 160 N to slide a box along the surface of a level floor at constant speed. The coefficient of static friction is 052, and the coefficient of kinetic
You find it takes 200 N of horizontal force to move an empty pickup truck along a level road at a speed of 2.4 m/s. You then load the pickup and pump up its tires so that its total weight increases
As shown in Fig. 5.54, block A (mass 2.25 kg) rests on a tabletop. It is connected by a horizontal cord passing over a light, frictionless pulley to a hanging block B (mass 130 kg). The coefficient
A 25.O-kg box of textbooks rests on a loading ramp that makes an angle a with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35. (a) As the
A large crate with mass m rests on a horizontal floor. The coefficients of friction between the crate and the floor are IL, and μk A woman pushes downward at an angle (J below the horizontal on
A box with mass m is dragged across a level floor having a coefficient of kinetic friction μk by a rope that is pulled upward at an angle (J above the horizontal with a force of magnitude F.
Blocks A, B, and C are placed as in Fig. 5.56 and connected by ropes of negligible mass. Both A and B weigh 25.0 N each, and the coefficient of kinetic friction between each block and the surface is
Starting from Eq. (5.10), derive Eqs. (5.11) and (5.12)
(a) In Example 5.19 (Section 5.3), what value of D is required to make Vt = 42 m/s for the skydiver? (b) If the skydiver's daughter, whose mass is 45 kg, is falling through the air and has the same D
You throw a baseball straight up. The drag force is proportional to v2. In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and (a) it is
A machine part consists of a thin 40.0-cm-Iong bar with small l.15-kg masses fastened by screws to its ends. The screws can support a maximum force of 75.0 N without pulling out. This bar rotates
A flat (unbanked) curve on a highway has a radius of 220.0 m. A car rounds the curve ata speed of 25.0 m/s. (a) What is the minimum coefficient of friction that will prevent sliding? (b) Suppose
A 1125-kg car and a 2250-kg pickup truck approach a curve on the expressway that has a radius of 225 m. (a) At what angle should the highway engineer bank this curve so that vehicles traveling at
The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end (Fig. 5.57). Each arm supports a seat suspended from a cable 5.00 m
In another version of the "Giant Swing" (see Exercise 5.52), the seat is connected to two cables as shown in Fig. 5.58, one of which is horizontal. The seat swings in a h0ri2ontal circle at a rate of
A small button placed on a horizontal rotating platform with diameter 0.320 m will revolve with the platform when it is brought up to a speed of 40.0 rev/min, provided the button is no more than
Rotating Space Stations One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a
The Cosmo clock 21 Ferris wheel in Yokohama City, Japan, has a diameter of 100 m. Its name comes from its 60 arms each of which can function as a second hand (so that it makes one revolution every
An airplane flies in a loop (a circular path in a vertical plane) of radius 150 m. The pilot's head always points toward the center of the loop. The speed of the airplane is not constant; the
A 50.0-kg stunt pilot who has been diving her all plane vertically pulls out of the dive by changing her course to a circle in a vertical plane. (a) If the plane's speed at the lowest point of the
Stay Dry! You tie a cord to a pail of water, and you swing the pail in a vertical circle of radius 0.600 m. What minimum speed must you give the pail at the highest point of the circle if no water is
A bowling ball weighing 71.2 N (16.0 Ib) is attached to the ceiling by a 3.80-m rope. The ball is pulled to one side and released; it then swings back and forth as a pendulum. As the rope swings
Two ropes are connected to a steel cable that supports a hanging weight as shown in Fig. 5.59.(a) Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to
In Fig. 5.60 a worker lifts a weight w by pulling down on a rope with a force F. The upper pulley is attached to the ceiling by a chain, and the lower pulley is attached to the weight by another
A Rope with Mass In most problems in this book, the ropes, cords, or cables have so little mass compared to other objects in the problem that you can safely ignore their mass. But if the rope is the
Another Rope with Mass A block wills mass M is attached to the lower end of a vertical, uniform rope with mass m and length L. A constant upward force F is applied to the top of the rope, causing the
A block with mass m, is placed on an inclined plane with slope angle a and is connected to a second hanging block with mass m2 by a cord passing over a small, frictionless pulley (Fig. 5.62). The
(a) Block A in Fig. 5.63 weighs 60.0 N. The coefficient of static friction between the block and the surface on which it rests is 0.25. The weight w is 12.0 N and the system is in equilibrium. Find
Block A in Fig. 5.64 weighs 1.20 N and block B weighs 3.60 N. The coefficient of kinetic friction between all surfaces is 0.300. Find the magnitude of the horizontal force F necessary to drag block B
A window washer pushes his scrub brush up a vertical window at constant speed by applyinga force F as shown in Fig. 5.65. The brush weighs 12.0 N and the coefficient of kinetic friction is μk =
The Flying Leap of Flea High-speed motion pictures (3500frames/second) of a jumping 210-μg flea yielded the data to plot the flea's acceleration as a function of time as shown in Fig. 5.66. (See
A 25,000-kg rocket blasts off vertically from the earth's surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant (see Chapter 12). Inside
You are standing on a bathroom scale in an elevator in a tall building. Your mass is 72 kg. The elevator starts from rest and travels upward with a speed that varies with time according to v(t) =
Elevator Design you are designing an elevator for a hospital. The force exerted on a passenger by the floor of the elevator is not to exceed 1.60 times the passenger's weight. The elevator
You are working for a shipping company. Your job is to stand at the bottom of a 8.0-m-Iong ramp that is inclined at 37° above the horizontal. You grab packages off a conveyor belt and propel them up
A hammer is hanging by a light rope from the ceiling of a bus. The ceiling of the bus is parallel to the roadway. The bus is traveling in a straight line on a horizontal street You observe that the
A steel washer is suspended inside an empty shipping crate from a light string attached to the top of the crate. The crate slides down a long ramp that is inclined at an angle of 37° above the
Lunch Time! You are riding your motorcycle one day down a wet street that slopes downward at an angle of 200 below the horizontal. As you start to ride down the hill, you notice a construction crew
In the system shown in Fig. 5.54, block A has mass mA, block B has mass mB' and the rope connecting them has a nonzero mass mole. The rope has a total length L, and the pulley has a very small
If the coefficient of static friction between a table and a uniform massive rope is μx, what fraction of the rope can hang over the edge of the table without the rope sliding?
A 30.0-kg packing case is initially at rest on the floor of a 1500-kg pickup truck. The coefficient of static friction between the case and the truck floor is 0.30, and the coefficient of kinetic
Traffic Court you are called as an expert witness in the trial of a traffic violation. The facts are these: A driver slammed on his brakes and came to a stop with constant acceleration. Measurements
Two identical 15.0-kg balls, each 25.0 cm in diameter, are suspended by two 35.lkm wires as shown in Fig. 5.67. The entire apparatus is supported by a single 18.1km wire, and the surfaces of the
Losing Cargo a 12.0-kg box rests on the flat floor of a truck. The coefficients of friction between the box and floor are μs, = 0.19 and μk = 0.15. The truck stops at a stop sign and then
Block A in Fig. 5.68 weighs 1.40 N, and block B weighs 4.20 N. The coefficient of kinetic friction between all surfaces is 0.30. Find the magnitude of the horizontal force F necessary to drag block B
You are part of a design team for future exploration of the planet Mars, where g = 3.7 m/s2. An explorer is to step out of a survey vehicle traveling horizontally at 33 m/s when it is 1200 m above
Block a in Fig. 5.69 has a mass of 4.00 kg, and block B has mass 12.0 kg. The coefficient of kinetic friction between block B and the horizontal surface is 0.25.(a) What is the mass of block C if
Two blocks connected by a cord passing over a small, frictionless pulley rest on frictionless planes (Fig. 5.70). (a) Which way will the system move when the blocks are released from rest? (b)
In terms of mb m2, and g, find the accelerations of each block in Fig. 5.71. There is no friction anywhere in the system.
Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop (Fig. 5.72). There is no friction between block A and the tabletop, but the coefficient of
Two objects wilt masses 5.00 kg and 2.00 kg hang 0.600 m above the floor from the ends of a cord 6.00 m long passing over a frictionless pulley. Bolt objects start from rest. Find the maximum height
Friction in an Elevator you are riding in an elevator on the way to the 181h floor of your dormitory. The elevator is accelerating upward with a = 1.90 mls2, beside you is 1he box containing your new
A block is placed against the vertical front of a cart as shown in Fig. 5.73. What acceleration must the cart have so that block A does not fall? The coefficient of static friction between the block
Two blocks with masses 4.00 kg and 8.00 kg are connected by a string and slide down a 30.0 inclined plane (Fig. 5.74). The coefficient of kinetic friction between the 4.0Q.kg block and the plane is
Block A with weight 3w, slides down an inclined plane S of slope angle 36.9° at a constant speed while plank B, with weight w, rests on top of A. The plank is attached by a cord to the wall (Fig.
Accelerometer the system shown in Fig. 5.76 can be used to measure 1he acceleration of 1he system. An observer riding on the platform measures the angle θ that the 1hread supporting the light
Banked Cone I A curve with a 120-m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s. what is the minimum coefficient of static
Banked Curve II Consider a wet roadway banked as in Example 5.23 (Section 5.4), where there is a coefficient of static friction of 0.30 and a coefficient of kinetic friction of 0.25 between the tires
Maximum Safe Speed As you travel every day to campus, the road makes a large tom that is approximately an arc of a circle. Youno1ice the warnings sign at the start of the tom, asking for a maximum
You are riding in a school bus. As the bus rounds a flat curve at constant speed, a lunch box with mass O.SOO kg, suspended from the ceiling of the bus by a string 1.80 m long, is found to hang at
The Monkey and Bananas Problem A 20-kg monkey has a firm hold on a light rope that passes over a frictionless pulley and is attached to a 20-kg bunch of bananas (Fig. 5.77). The monkey looks up, sees
You throw a rock downward into water with a speed of 3mglk, where k is the coefficient in Eq. (5.7). Assume that the relationship between fluid resistance and speed is as given in Eq. (5.7), and
A rock with mass m = 3.00 kg falls from rest in a viscous medium. The rock is acted on by a net constant downward force of 18.0 N (a combination of gravity and the buoyant force exerted by the
A rock with mass m slides with initial velocity Vo on a horizontal surface. A retarding force FR that the surface exerts on the rock is proportional to the square root of the instantaneous velocity
A fluid exerts an upward buoyancy force on an object immersed in it. In the derivation of Eq. (5.9) the buoyancy force exerted on an object by the fluid was ignored. But in some situations, where the
The 4.00-kg block in Figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the diagram and the tension
Equation (5.10) applies to the case where the initial velocity is zero. (a) Derive the corresponding equation for v,(t) when the falling object has an initial downward velocity with magnitude
A small rock moves in water, and the force exerted on it by the water is given by Eq. (5.7). The terminal speed of the rock is measured and found to be 2.0 m/s. The rock is projected upward at an
You observe a 1350-kg sports car rolling along flat pavement in a straight line. The only horizontal forces acting on it are a constant rolling friction and air resistance (proportional to the square
A 70-kg person ride in a 30-kg cart moving at 12 m/s at the top of a hill that is in the shape of an arc of a circle with a radius of 40 m. (a) What is the apparent weight of the person as the cart
Merry-Go-Round One December identical twins Jena and Jackie are playing on a large merry-go-round (a disk mounted parallel to the ground, on a vertical axle through its center) in their school
A passenger with mass 85 kg rides in a Ferris wheel like that in Example 5.24 (Section 5.4). The seats travel in a circle of radius 35 m. The Ferris wheel rotates at constant speed and makes one
On the ride "Spindle top" at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it
A physics major is working to pay his college tuition by performing in a traveling carnival. He rides a motorcycle inside a hollow transparent plastic sphere. After gaining sufficient speed, he
Ulterior Motives You are driving a classic 1954 Nash Ambassador with a friend who is sitting to your right on the passenger side of the front seat. The Ambassador has flat bench seats. You would like
A small block with mass m rests on a frictionless horizontal tabletop a distance r from a hole in the center of the table (Fig. 5.79). A string tied to the small block passes down through the hole,
A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/s about a vertical diameter (Fig
A model airplane with mass 2.20 kg moves in the xy-plane such that its x- and y-coordinates vary in time according to x(t) = a - pt' and yet) = -yt - lit2 , where a = I.S0m, p = 0.120 m/s, -y = 3.00
A particle moves on a frictionless surface along a path as shown in Fig. 5.81. (The figure gives a view looking down on the surface.) The particle is initially at rest at point A and then begins to
A small remote-control car with mass 1.60 kg moves at a constant speed of v = 12.0 m/ s in a vertical circle inside a hollow metal cylinder that has a radius of 5.00 m (Fig 5.82). What is the
A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (Fig. 5.83). The walls of the cone make an
Moving Wedge A wedge with mass M rests on a frictionless, horizontal tabletop. A block with mass m is placed on the wedge (Fig. S.84a). There is no friction between the block and the wedge. The
A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge (Fig. S.84b). What must the magnitude of F
A box of weight w is accelerated up a ramp by a rope that exerts a tension T. The ramp makes an angle a with the horizontal, and the rope makes an angle 6 above the ramp. The coefficient of kinetic
Angle for Minimum Force. A box with weight w is pulled at constant speed along a level floor by a force F that is at an angle 6 above the h0ri2ontal. The coefficient of kinetic friction between the
Falling Baseball You drop a baseball from the roof of a tall building. As the ball falls, the air exerts a drag force proportional to the square of the ball's speed (f= Dv2).(a) In a diagram, show
Double Atwood's Machine In Fig. 5.85 masses ml and m2 are connected by a light string A over a light, frictionless pulley B. The axle of pulley B is connected by a second light string Cover a second
The masses of blocks A and B in Fig. 5.86 are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on the floor and are connected by a mass less string passing over a mass less and
A ball is held at rest at position A in Fig. 5.87 by two light strings. The horizontal string is cut and the ball starts swinging as a pendulum. Point B is the farthest to the right the ball goes as
An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise
A tow truck pulls a car 5.00 km along a horizontal roadway using a cable having a tension of 850 N. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at 35.0o
A factory worker pushes a 30.O-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor
Suppose the worker in Exercise 6.3 pushes downward at an angle of 30° below the horizontal. (a) What magnitude of force must the worker apply to move the crate at constant velocity? (b) How much
A 75.O-kg painter climbs a ladder that is 2.75 m long leaning against a vertical wall. The ladder makes an 30.0° angle with the wall. (a) How much work does gravity do on the painter? (b) Does
Two tugboats pill a disabled supertanker. Each tug exerts a constant force of 1.80 X I (fN, one 14° west of north and the other 14° east of north, as they pull the tanker 0.75 km toward the north.
Two blocks are connected by a very light string passing over a mass less and frictionless pulley (Figure 6.30). Traveling at constant speed, the 20.0-N block moves 75.0 cm to the right and the 12.0-N

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