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physics
mechanics

Questions and Answers of Mechanics

A simple pendulum, which we will consider in detail in Chapter 15, consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has
An object of mass m starts from rest and slides a distance d down a frictionless incline of angle &. While sliding, it contacts an unstressed spring of negligible mass as shown in Figure P8.10. The
The system shown in Figure P8.20 consists of a light inextensible cord, light frictionless pulleys, and blocks of equal mass. It is initially held at rest so that the blocks are at the same height
A block of mass 0.250 kg is placed on top of a light vertical spring of force constant 5 000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from
A circus trapeze consists of a bar suspended by two parallel ropes, each of length L, allowing performers to swing in a vertical circular arc (Figure P8.12). Suppose a performer with mass m holds the
Two objects are connected by a light string passing over a light frictionless pulley as shown in Figure P8.13. The object of mass 5.00 kg is released from rest. Using the principle of conservation of
Two objects are connected by a light string passing over a light frictionless pulley as in Figure P8.13. The object of mass m1 is released from rest at height h. using the principle of conservation
A light rigid rod is 77.0 cm long. Its top end is pivoted on a low-friction horizontal axle. The rod hangs straight down at rest with a small massive ball attached to its bottom end. You strike the
Air moving at 11.0 m/s in a steady wind encounters a windmill of diameter 2.30 m and having an efficiency of 27.5%. The energy generated by the windmill is used to pump water from a well 35.0 m deep
A 20.0-kg cannon ball is fired from a cannon with muzzle speed of 1 000 m/s at an angle of 37.0° with the horizontal. A second ball is fired at an angle of 90.0°. Use the conservation of energy
A daredevil plans to bungee-jump from a balloon 65.0 m above a carnival midway (Figure P8.19). He will use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 10.0
A 4.00-kg particle moves from the origin to position C, having coordinates x = 5.00 m and y = 5.00 m. One force on the particle is the gravitational force acting in the negative y direction (Fig.
(a) Suppose that a constant force acts on an object. The force does not vary with time, nor with the position or the velocity of the object. Start with the general definition for work done by a force
A force acting on a particle moving in the xy plane is given by F = (2yi + x2j), where x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.00 m and
A particle of mass m = 5.00 kg is released from point A and slides on the frictionless track shown in Figure P8.24. Determine (a) The particle€™s speed at points B and C and (b) The net
A single constant force F = (3i +5j) acts on a 4.00-kg particle. (a) Calculate the work done by this force if the particle moves from the origin to the point having the vector position r = (2i
At time ti, the kinetic energy of a particle is 30.0 J and the potential energy of the system to which it belongs is 10.0 J. At some later time tf, the kinetic energy of the particle is 18.0 J. (a)
In her hand a softball pitcher swings a ball of mass 0.250 kg around a vertical circular path of radius 60.0 cm before releasing it from her hand. The pitcher maintains a component of force on the
An electric scooter has a battery capable of supplying 120 Wh of energy. If friction forces and other losses account for 60.0% of the energy usage, what altitude change can a rider achieve when
The world’s biggest locomotive is the MK5000C, a behemoth of mass 160 metric tons driven by the most powerful engine ever used for rail transportation, a Caterpillar diesel capable of 5 000 hp.
A 70.0-kg diver steps off a 10.0-m tower and drops straight down into the water. If he comes to rest 5.00 m beneath the surface of the water, determine the average resistance force exerted by the
A single conservative force acting on a particle varies as F = (-Ax + Bx2) i N, where A and B are constants and x is in meters. (a) Calculate the potential-energy function U(x) associated with this
A uniform board of length L is sliding along a smooth (frictionless) horizontal plane as in Figure P8.39a. The board then slides across the boundary with a rough horizontal surface. The coefficient
A 75.0-kg sky surfer is falling straight down with terminal speed 60.0 m/s. Determine the rate at which the sky surfer–Earth system is losing mechanical energy.
A 1.50-kg object is held 1.20 m above a relaxed mass less vertical spring with a force constant of 320 N/m. The object is dropped onto the spring. (a) How far does it compress the spring? (b)
A 50.0-kg block and a 100-kg block are connected by a string as in Figure P8.36. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between the 50.0 kg block and
A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired the ball moves 15.0 cm
An 80.0-kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens the parachute at an altitude of 200 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N
A 5.00-kg block is set into motion up an inclined plane with an initial speed of 8.00 m/s (Fig. P8.33). The block comes to rest after traveling 3.00m along the plane, which is inclined at an angle of
A boy in a wheelchair (total mass 47.0 kg) wins a race with a skateboarder. The boy has speed 1.40 m/s at the crest of a slope 2.60 m high and 12.4 m long. At the bottom of the slope his speed is
The coefficient of friction between the 3.00-kg block and the surface in Figure p8.31 is 0.4000. The system starts from rest. What is the speed of the 5.00-kg ball when it has fallen 1.50 m?
A single conservative force acts on a 5.00-kg particle. The equation Fx = (2x + 4) N describes the force, where x is in meters. As the particle moves along the x axis from x = 1.00 m to x = 5.00 m,
A potential-energy function for a two-dimensional force is of the form U = 3x3y - 7x. Find the force that acts at the point (x, y).
The potential energy of a system of two particles separated by a distance r is given by U(r) = A/r, where A is a constant. Find the radial force Fr that each particle exerts on the other.
A right circular cone can be balanced on a horizontal surface in three different ways. Sketch these three equilibrium configurations, and identify them as positions of stable, unstable, or neutral
For the potential energy curve shown in Figure (a) Determine whether the force Fx is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral
A particle moves along a line where the potential energy of its system depends on its position r as graphed in Figure P8.46. In the limit as r increases without bound, U(r) approaches %1 J. (a)
A particle of mass 1.18 kg is attached between two identical springs on a horizontal frictionless tabletop. The springs have force constant k and each is initially unstressed. (a) If the particle
A block slides down a curved frictionless track and then up an inclined plane as in Figure P8.48. The coefficient of kinetic friction between block and incline is μk. Use energy methods to show
Make an order-of-magnitude estimate of your power output as you climb stairs. In your solution, state the physical quantities you take as data and the values you measure or estimate for them. Do you
The mass of a car is 1 500 kg. The shape of the body is such that its aerodynamic drag coefficient is D = 0.330 and the frontal area is 2.50 m2. Assuming that the drag force is proportional to v2 and
Assume that you attend a state university that started out as an agricultural college. Close to the center of the campus is a tall silo topped with a hemispherical cap. The cap is frictionless when
A 200-g particle is released from rest at point A along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30.0 cm (Fig. P8.52). Calculate (a) The
What If? The particle described in Problem 52 (Fig. P8.52) is released from rest at A, and the surface of the bowl is rough. The speed of the particle at B is 1.50 m/s. (a) What is its kinetic
A 2.00-kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m (Fig. P8.54). The pulley is frictionless. The block is released from rest
Suppose the incline is frictionless for the system described in Problem 54 (Fig. P8.54). The block is released from rest with the spring initially unstretched. (a) How far does it move down the
A child€™s pogo stick (Fig P8.56) stores energy in a spring with a force constant of 2.50 0 104 N/m. At position A (xA = ─ 0.100 m), the spring compression is a maximum and the child
A 10.0-kg block is released from point A in Figure P8.57. The track is frictionless except for the portion between points A and B, which has a length of 6.00 m. The block travels down the track, hits
The potential energy function for a system is given by U(x) = ─x3 % 2x2 % 3x. (a) Determine the force Fx as a function of x. (b) For what values of x is the force equal to zero? (c) Plot
A 20.0-kg block is connected to a 30.0-kg block by a string that passes over a light frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of
A 1.00-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P8.60). The object has a speed of vi = 3.00 m/s when it makes contact with a light spring that
A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x (Fig. P8.61). The force constant of the spring is 450 N/m. When it is
A uniform chain of length 8.00 m initially lies stretched out on a horizontal table. (a) If the coefficient of static friction between chain and table is 0.600, show that the chain will begin to
A child slides without friction from a height h along a curved water slide (Fig. P8.63). She is launched from a height h/5 into the pool. Determine her maximum airborne height y in terms of h and
A 1.00-kg glider on a horizontal air track is pulled by a string at angle &. The taut string runs over a light pulley at height h0 = 40.0 cm above the line of motion of the glider. The other end of
Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with man-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force
A 5.00-kg block free to move on a horizontal, frictionless surface is attached to one end of a light horizontal spring. The other end of the spring is held fixed. The spring is compressed 0.100 m
A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass (which we will study in Chapter 9). As in Figure P8.67, the skateboarder starts from rest in
A block of mass M rests on a table. It is fastened to the lower end of a light vertical spring. The upper end of the spring is fastened to a block of mass m. The upper block is pushed down by an
A ball having mass m is connected by a strong string of length L to a pivot point and held in place in a vertical position. A wind exerting constant force of magnitude F is blowing from left to right
A ball is tied to one end of a string. The other end of the string is held fixed. The ball is set moving around a vertical circle without friction, and with speed at the top of the circle, as in
A ball whirls around in a vertical circle at the end of a string. If the total energy of the ball–Earth system remains constant, show that the tension in the string at the bottom is greater than
A pendulum, comprising a string of length L and a small sphere, swings in the vertical plane. The string hits a peg located a distance d below the point of suspension (Fig. P8.72) (a) Show that if
A roller-coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller coaster shown in Figure P8.73 has a circular loop of radius R in a
In 1887 in Bridgeport, Connecticut, C. J. Belknap built the water slide shown in Figure P8.74. A rider on a small sled, of total mass 80.0 kg, pushed off to start at the top of the slide (point C)
Determine the order of magnitude of the gravitational force that you exert on another person 2 m away. In your solution state the quantities you measure or estimate and their values.
Two ocean liners, each with a mass of 40 000 metric tons, are moving on parallel courses, 100 m apart. What is the magnitude of the acceleration of one of the liners toward the other due to their
A 200-kg object and a 500-kg object are separated by 0.400 m. (a) Find the net gravitational force exerted by these objects on a 50.0-kg object placed midway between them. (b) At what position
Two objects attract each other with a gravitational force of magnitude 1.00 X 10─8 N when separated by 20.0 cm. If the total mass of the two objects is 5.00 kg, what is the mass of each?
Three uniform spheres of mass 2.00 kg, 4.00 kg, and 6.00 kg are placed at the corners of a right triangle as in Figure P13.5. Calculate the resultant gravitational force on the 4.00-kg object,
During a solar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Moon between the Earth and the Sun. (a) What force is exerted by the Sun on the Moon? (b) What force is exerted
In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.50 kg and 15.0 g whose centers are separated by about
A student proposes to measure the gravitational constant G by suspending two spherical objects from the ceiling of a tall cathedral and measuring the deflection of the cables from the vertical. Draw
When a falling meteoroid is at a distance above the Earth’s surface of 3.00 times the Earth’s radius, what is its acceleration due to the Earth’s gravitation?
The free-fall acceleration on the surface of the Moon is about one sixth of that on the surface of the Earth. If the radius of the Moon is about 0.250RE, find the ratio of their average densities,
On the way to the Moon the Apollo astronauts reached a point where the Moon’s gravitational pull became stronger than the Earth’s. (a) Determine the distance of this point from the center of
The center-to-center distance between Earth and Moon is 384 400 km. The Moon completes an orbit in 27.3 days. (a) Determine the Moon’s orbital speed. (b) If gravity were switched off, the Moon
Plaskett€™s binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This means that the masses of the two star are equal (Fig.
A particle of mass m moves along a straight line with constant speed in the x direction, a distance b from the x axis (Fig. P13.14). Show that Kepler€™s second law is satisfied by showing
Io, a moon of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 X 105 km. From these data, determine the mass of Jupiter.
The Explorer VIII satellite, placed into orbit November 3, 1960, to investigate the ionosphere, had the following orbit parameters: perigee, 459 km; apogee, 2 289 km (both distances above the
Comet Halley (Figure P13.17) approaches the Sun to within 0.570 AU, and its orbital period is 75.6 years. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean
Two planets X and Y travel counterclockwise in circular orbits about a star as in Figure P13.18. The radii of their orbits are in the ratio 3:1. At some time, they are aligned as in Figure P13.18a,
A synchronous satellite, which always remains above the same point on a planet’s equator, is put in orbit around Jupiter to study the famous red spot. Jupiter rotates about its axis once every 9.84
Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose that the mass of a certain spherical neutron star is twice the
Suppose the Sun’s gravity were switched off. The planets would leave their nearly circular orbits and fly away in straight lines, as described by Newton’s first law. Would Mercury ever be farther
As thermonuclear fusion proceeds in its core, the Sun loses mass at a rate of 3.64 X 109 kg/s. During the 5 000-yr period of recorded history, by how much has the length of the year changed due to
Three objects of equal mass are located at three corners of a square of edge length l as in Figure P13.23. Find the gravitational field at the fourth corner due to these objects.
A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. It has strayed too close to a black hole having a mass 100 times that of the Sun (Fig.
Compute the magnitude and direction of the gravitational field at a point P on the perpendicular bisector of the line joining two objects of equal mass separated by a distance 2a as shown in Figure
A satellite of the Earth has a mass of 100 kg and is at an altitude of 2.00 x 106 m. (a) What is the potential energy of the satellite” Earth system? (b) What is the magnitude of the
How much energy is required to move a 1 000-kg object from the Earth’s surface to an altitude twice the Earth’s radius?
At the Earth’s surface a projectile is launched straight up at a speed of 10.0 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth.
After our Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state, in which it has approximately the same mass as it has now, but a radius equal to the radius of
How much work is done by the Moon’s gravitational field as a 1 000-kg meteor comes in from outer space and impacts on the Moon’s surface?
A system consists of three particles, each of mass 5.00 g, located at the corners of an equilateral triangle with sides of 30.0 cm. (a) Calculate the potential energy of the system. (b) If the
An object is released from rest at an altitude h above the surface of the Earth. (a) Show that its speed at a distance r from the Earth’s center, where RE < r < RE + h, is given by (b) Assume
A space probe is fired as a projectile from the Earth’s surface with an initial speed of 2.00 X 104 m/s. What will its speed be when it is very far from the Earth? Ignore friction and the rotation
(a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at the Earth’s orbit? (b) Voyager 1 achieved a maximum speed of 125 000 km/h
A €œtreetop satellite€ (Fig P13.35) moves in a circular orbit just above the surface of a planet, assumed to offer no air resistance. Show that its orbital speed v and the escape

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