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physics
mechanics

Questions and Answers of Mechanics

If the coefficient of static friction between your coffee cup and the horizontal dashboard of your car is μs = 0.800, how fast can you drive on a horizontal roadway around a right turn of radius
A 0.500-kg object is suspended from the ceiling of an accelerating boxcar as in Figure 6.13. If a = 3.00 m/s2, find (a) The angle that the string makes with the vertical and (b) The tension in the
A small container of water is placed on a carousel inside a microwave oven, at a radius of 12.0 cm from the center. The turntable rotates steadily, turning through one revolution in each 7.25 s. What
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591 N. As the elevator later stops, the scale reading is 391 N. Assume the magnitude of the
The Earth rotates about its axis with a period of 24.0 h. Imagine that the rotational speed can be increased. If an object at the equator is to have zero apparent weight, (a) What must the new
A small block is at rest on the floor at the front of a railroad boxcar that has length L. The coefficient of kinetic friction between the floor of the car and the block is μ k. The car,
A student stands in an elevator that is continuously accelerating upward with acceleration a. Her backpack is sitting on the floor next to the wall. The width of the elevator car is L. The student
A child on vacation wakes up. She is lying on her back. The tension in the muscles on both sides of her neck is 55.0 N as she raises her head to look past her toes and out the motel window. Finally
One popular design of a household juice machine is a conical, perforated stainless steel basket 3.30 cm high with a closed bottom of diameter 8.00 cm and open top of diameter 13.70 cm that spins at
A plumb bob does not hang exactly along a line directed to the center of the Earth’s rotation. How much does the plumb bob deviate from a radial line at 35.0° north latitude? Assume that the
A sky diver of mass 80.0 kg jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s. (a) What is the acceleration of the sky diver when her speed is 30.0 m/s? What is the drag
A small piece of Styrofoam packing material is dropped from a height of 2.00 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g ─ bv. After
(a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm3) falling through air if its radius is 8.00 cm and its drag coefficient is 0.500. (b) From what height would a freely falling
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
A fire helicopter carries a 620-kg bucket at the end of a cable 20.0 m long as in Figure P6.36. As the helicopter flies to a fire at a constant speed of 40.0 m/s, the cable makes an angle of 40.0°
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
The mass of a sports car is 1 200 kg. The shape of the body 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
A motorboat cuts its engine when its speed is 10.0 m/s and coasts to rest. The equation describing the motion of the motorboat during this period is v = vie-ct, where v is the speed at time t, vi is
Consider an object on which the net force is a resistive force proportional to the square of its speed. For example, assume that the resistive force acting on a speed skater is f = ─ kmv2,
(a) Use the result of Problem 40 to find the position x as a function of time for an object of mass m, located at x = 0 and moving with velocity v0i at time t = 0 and thereafter experiencing a net
At major league baseball games it is commonplace to flash on the scoreboard a speed for each pitch. This speed is determined with a radar gun aimed by an operator positioned behind home plate. The
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. What is the order of magnitude of this force? In your solution state the quantities you
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 = 0.030 0 kg/s. (a) Calculate
A hailstone of mass 4.80 x 10-4 kg falls through the air and experiences a net force given by F = ─ mg + Cv2 Where C = 2.50 x 10-5 kg/m. (a) Calculate the terminal speed of the hailstone.
A 0.142-kg baseball has a terminal speed of 42.5 m/s (95 mi/h). (a) If a baseball experiences a drag force of magnitude R = Cv2, what is the value of the constant C? (b) What is the magnitude of
A 50.0-kg parachutist jumps from an airplane and falls to Earth with a drag force proportional to the square of the speed, R = Cv2. Take C = 0.200 kg/m (with the parachute closed) and C = 20.0 kg/m
Consider a 10.0-kg projectile launched with an initial speed of 100 m/s, at an elevation angle of 35.0°. The resistive force is R = θbv, where b = 10.0 kg/s. (a) Use a numerical method to
A professional golfer hits her 5-iron 155 m (170 yd). A 46.0-g golf ball experiences a drag force of magnitude R = Cv2, and has a terminal speed of 44.0 m/s. (a) Calculate the drag constant C for
In a home laundry dryer, a cylindrical tub containing wet clothes is rotated steadily about a horizontal axis, as shown in Figure P6.50. So that the clothes will dry uniformly, they are made to
We will study the most important work of Nobel laureate Arthur Compton in Chapter 40. Disturbed by speeding cars outside the physics building at Washington University in St. Louis, Compton designed a
A car of mass m passes over a bump in a road that follows the arc of a circle of radius R as in Figure P6.51. (a) What force does the road exert on the car as the car passes the highest point of
Interpret the graph in Figure 6.18(b). Proceed as follows: (a) Find the slope of the straight line, including its units. (b) From Equation 6.6, R=1/2DpAv2, identify the theoretical slope of a
A student builds and calibrates an accelerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a protractor that she
(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
Because the Earth rotates about its axis, a point on the equator experiences a centripetal acceleration of 0.033 7 m/s2, while a point at the poles experiences no centripetal acceleration. (a) Show
An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a hole in the center of the
Suppose the boxcar of Figure 6.13 is moving with constant acceleration a up a hill that makes an angle θ with the horizontal. If the pendulum makes a constant angle θ with the perpendicular
The pilot of an airplane executes a constant-speed loop-the loop maneuver in a vertical circle. The speed of the airplane is 300 mi/h, and the radius of the circle is 1 200 ft. (a) What is the
A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk (Fig. P6.60). The coefficients of friction between block and disk are 0.750 (static) and 0.640 (kinetic) while those
A space station, in the form of a wheel 120 m in diameter, rotates to provide an “artificial gravity” of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of
An amusement park ride consists of a rotating circular platform 8.00 m in diameter from which 10.0-kg seats are suspended at the end of 2.50-m mass less chains (Fig. P6.63). When the system rotates,
A piece of putty is initially located at point A on the rim of a grinding wheel rotating about a horizontal axis. The putty is dislodged from point A when the diameter through A is horizontal. It
An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough such that any person inside is held up against the wall when the floor drops away (Fig. P6.65). The
An example of the Coriolis effect supposes air resistance is negligible for a golf ball. A golfer tees off from a location precisely at θi = 35.0° north latitude. He hits the ball due south, with
An example of the Coriolis effect supposes air resistance is negligible for a golf ball. A golfer tees off from a location precisely at θi = 35.0° north latitude. He hits the ball due south,
A car rounds a banked curve as in Figure 6.6. The radius of curvature of the road is R, the banking angle is θ, and the coefficient of static friction is μs. (a) Determine the range of
A single bead can slide with negligible friction on a wire that is bent into a circular loop of radius 15.0 cm, as in Figure P6.68. The circle is always in a vertical plane and rotates steadily about
The expression F = arv + br 2v 2 gives the magnitude of the resistive force (in newtons) exerted on a sphere of radius r (in meters) by a stream of air moving at speed v (in meters per second), where
A 9.00-kg object starting from rest falls through a viscous medium and experiences a resistive force R = ─bv, where v is the velocity of the object. If the object reaches one-half its terminal
A model airplane of mass 0.750 kg flies in a horizontal circle at the end of a 60.0-m control wire, with a speed of 35.0 m/s. Compute the tension in the wire if it makes a constant angle of 20.0°
Members of a skydiving club were given the following data to use in planning their jumps. In the table, d is the distance fallen from rest by a sky diver in a “free-fall stable spread position,”
If a single constant force acts on an object that moves on a straight line, the object’s velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time,
A roller coaster at the Six Flags Great America amusement park in Gurnee, IL, incorporates some clever design technology and some basic physics. Each vertical loop, instead of being circular, is
Given M = 6i + 2j ─k and N = 2i ─j─3k, calculate the vector product M X N.
The vectors 42.0 cm at 15.0° and 23.0 cm at 65.0° both start from the origin. Both angles are measured counterclockwise from the x axis. The vectors form two sides of a parallelogram. (a) Find
Two vectors are given by A =─3i + 4j and B = 2i + 3j. Find (a) A = B and (b) the angle between A and B.
Two vectors are given by A = ─ 3i + 7j ─ 4k and B = 6i ─ 10j + 9k. Evaluate the quantities (a) cos─1 [A∙B/AB] and (b) sin─1 [|A X B|/AB]. (c) Which give(s) the
The wind exerts on a flower the force 0.785 N horizontally to the east. The stem of the flower is 0.450 m long and tilts toward the east, making an angle of 14.0° with the vertical. Find the vector
A student claims that she has found a vector A such that (2i ─ 3j + 4k) X A = (4i + 3j ─k). Do you believe this claim? Explain.
If |A X B| = A∙B, what is the angle between A and B?
A particle is located at the vector position r = (i + 3j) m, and the force acting on it is F = (3i + 2j) N. What is the torque about (a) the origin and (b) the point having coordinates (0, 6) m?
Two forces F1 and F2 act along the two sides of an equilateral triangle as shown in Figure P11.9. Point O is the intersection of the altitudes of the triangle. Find a third force F3 to be applied at
Use the definition of the vector product and the definitions of the unit vectors i, j, and k to prove Equations 11.7. You may assume that the x axis points to the right, the y axis up, and the z axis
A light rigid rod 1.00 m in length joins two particles, with masses 4.00 kg and 3.00 kg, at its ends. The combination rotates in the xy plane about a pivot through the center of the rod (Fig.
A 1.50-kg particle moves in the xy plane with a velocity of v = (4.20i ─ 3.60j) m/s. Determine the angular momentum of the particle when its position vector is r = (1.50i + 2.20 j) m.
The position vector of a particle of mass 2.00 kg is given as a function of time by r = (6.00i + 5.00tj) m. Determine the angular momentum of the particle about the origin, as a function of time.
A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in Figure P11.14. During the motion, the supporting wire of length l maintains the constant
A particle of mass m moves in a circle of radius R at a constant speed v, as shown in Figure P11.15. If the motion begins at point Q at time t = 0, determine the angular momentum of the particle
A 4.00-kg counterweight is attached to a light cord, which is wound around a spool (refer to Fig. 10.20). The spool is a uniform solid cylinder of radius 8.00 cm and mass 2.00 kg. (a) What is the
A particle of mass m is shot with an initial velocity vi making an angle θ with the horizontal as shown in Figure P11.17. The particle moves in the gravitational field of the Earth. Find the
Heading straight toward the summit of Pike’s Peak, an airplane of mass 12 000 kg flies over the plains of Kansas at nearly constant altitude 4.30 km, with a constant velocity of 175 m/s west? (a)
A ball having mass m is fastened at the end of a flagpole that is connected to the side of a tall building at point P shown in Figure P11.19. The length of the flagpole is l and it makes an angle
A fireman clings to a vertical ladder and directs the nozzle of a hose horizontally toward a burning building. The rate of water flow is 6.31 kg/s, and the nozzle speed is 12.5 m/s. The hose passes
Show that the kinetic energy of an object rotating about a fixed axis with angular momentum L = I) can be written as K = L2/2I.
A uniform solid sphere of radius 0.500 m and mass 15.0 kg turns counterclockwise about a vertical axis through its center. Find its vector angular momentum when its angular speed is 3.00 rad/s.
A uniform solid disk of mass 3.00 kg and radius 0.200 m rotates about a fixed axis perpendicular to its face. If the angular frequency of rotation is 6.00 rad/s, calculate the angular momentum of the
Big Ben (Figure P10.40), the Parliament Building tower clock in London, has hour and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg and 100 kg, respectively. Calculate the total
A particle of mass 0.400 kg is attached to the 100-cm mark of a meter stick of mass 0.100 kg. The meter stick rotates on a horizontal, frictionless table with an angular speed of 4.00 rad/s.
The distance between the centers of the wheels of a motorcycle is 155 cm. The center of mass of the motorcycle, including the biker, is 88.0 cm above the ground and halfway between the wheels. Assume
A space station is constructed in the shape of a hollow ring of mass 5.00 ' 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with
A cylinder with moment of inertia I1 rotates about a vertical, frictionless axle with angular speed ώi. A second cylinder, this one having moment of inertia I2 and initially not rotating, drops
A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg •m2 and is rotating at 10.0 rev/min about a frictionless vertical axle. Facing the axle, a 25.0-kg child hops
A student sits on a freely rotating stool holding two weights, each of mass 3.00 kg (Figure P11.30). When his arms are extended horizontally, the weights are 1.00 m from the axis of rotation and he
A uniform rod of mass 100 g and length 50.0 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small beads, each of mass 30.0 g, are mounted on the rod
An umbrella consists of a circle of cloth, a thin rod with the handle at one end and the center of the cloth at the other end, and several straight uniform ribs hinged to the top end of the rod and
A 60.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 500 kg •m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a
A puck of mass 80.0 g and radius 4.00 cm slides along an air table at a speed of 1.50 m/s as shown in Figure P11.34a, It makes a glancing collision with a second puck of radius 6.00 cm and mass 120 g
A wooden block of mass M resting on a frictionless horizontal surface is attached to a rigid rod of length θ and of negligible mass (Fig. P11.35) The rod is pivoted at the other end. A bullet
A space station shaped like a giant wheel has a radius of 100 m and a moment of inertia of 5.00 X 108 kg ∙ m2. A crew of 150 is living on the rim, and the station’s rotation causes the crew
A wad of sticky clay with mass m and velocity vi is fired at a solid cylinder of mass M and radius R (Figure P11.37). The cylinder is initially at rest and is mounted on a fixed horizontal axle
A thin uniform rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kg and its vertical
Suppose a meteor of mass 3.00 X 1013 kg, moving at 30.0 km/s relative to the center of the Earth, strikes the Earth. What is the order of magnitude of the maximum possible decrease in the angular
A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 20.0 kg ∙ m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the
The angular momentum vector of a processing gyroscope sweeps out a cone, as in Figure 11.14b. Its angular speed, called its processional frequency, is given by ώp = π/L, where + is the
In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius 0.529 x 10─10 m around the proton. Assuming the orbital angular momentum of the electron is equal to
We have all complained that there aren’t enough hours in a day. In an attempt to change that, suppose that all the people in the world line up at the equator, and all start running east at 2.50 m/s
A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass. As shown in Figure P8.67 on page 248, the skateboarder starts from rest in a crouching
A rigid, mass less rod has three particles with equal masses attached to it as shown in Figure P11.45. The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod
A 100-kg uniform horizontal disk of radius 5.50 m turns without friction at 2.50 rev/s on a vertical axis through its center, as in Figure P11.46, A feedback mechanism senses the angular speed of the
Comet Halley moves about the Sun in an elliptical orbit, with its closest approach to the Sun being about 0.590 AU and its greatest distance 35.0 AU (1 AU = the Earth–Sun distance). If the

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