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physics
mechanics

Questions and Answers of Mechanics

A 500-kg satellite is in a circular orbit at an altitude of 500 km above the Earth’s surface. Because of air friction, the satellite eventually falls to the Earth’s surface, where it hits the
A satellite of mass 200 kg is placed in Earth orbit at a height of 200 km above the surface. (a) With a circular orbit, how long does the satellite take to complete one orbit? (b) What is the
A satellite of mass m, originally on the surface of the Earth, is placed into Earth orbit at an altitude h. (a) With a circular orbit, how long does the satellite take to complete one orbit? (b)
A 1 000-kg satellite orbits the Earth at a constant altitude of 100 km. How much energy must be added to the system to move the satellite into a circular orbit with altitude 200 km?
The planet Uranus has a mass about 14 times the Earth’s mass, and its radius is equal to about 3.7 Earth radii. (a) By setting up ratios with the corresponding Earth values, find the free-fall
Determine the escape speed for a rocket on the far side of Ganymede, the largest of Jupiter€™s moons (Figure P13.41). The radius of Ganymede is 2.64 X 106 m, and its mass is 1.495 X 1023
In Robert Heinlein’s “The Moon is a Harsh Mistress,” the colonial inhabitants of the Moon threaten to launch rocks down onto the Earth if they are not given independence (or at least
An object is fired vertically upward from the surface of the Earth (of radius RE) with an initial speed vi that is comparable to but less than the escape speed vesc. (a) Show that the object
Derive an expression for the work required to move an Earth satellite of mass m from a circular orbit of radius 2RE to one of radius 3RE.
A comet of mass 1.20 X 1010 kg moves in an elliptical orbit around the Sun. Its distance from the Sun ranges between 0.500 AU and 50.0 AU. (a) What is the eccentricity of its orbit? (b) What is
A satellite moves around the Earth in a circular orbit of radius r. (a) What is the speed v0 of the satellite? Suddenly, an explosion breaks the satellite into two pieces, with masses m and 4m.
The Solar and Heliospheric Observatory (SOHO) spacecraft has a special orbit, chosen so that its view of the Sun is never eclipsed and it is always close enough to the Earth to transmit data easily.
Let ΔM represent the difference in the gravitational fields produced by the Moon at the points on the Earth’s surface nearest to and farthest from the Moon. Find the fraction ΔM/g, where
Two identical hard spheres, each of mass m and radius r, are released from rest in otherwise empty space with their centers separated by the distance R. They are allowed to collide under the
Two spheres having masses M and 2M and radii R and 3R, respectively, are released from rest when the distance between their centers is 12R. How fast will each sphere be moving when they collide?
An energy-efficient light-bulb, taking in 28.0 W of power, can produce the same level of brightness as a conventional bulb operating at power 100 W. The lifetime of the energy efficient bulb is 10
Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is one kilocalorie defined as 1 kcal = 4 186 J. Metabolizing one gram of fat can release 9.00 kcal. A
For saving energy, bicycling and walking are far more efficient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h a cyclist uses food energy at a rate of
Suppose the empty car described in Table 7.2 has a fuel economy of 6.40 km/liter (15 mi/gal) when traveling at 26.8 m/s (60 mi/h). Assuming constant efficiency, determine the fuel economy of the car
A compact car of mass 900 kg has an overall motor efficiency of 15.0%. (That is, 15% of the energy supplied by the fuel is delivered to the wheels of the car.) (a) If burning one gallon of gasoline
A baseball outfielder throws a 0.150-kg baseball at a speed of 40.0 m/s and an initial angle of 30.0°. What is the kinetic energy of the baseball at the highest point of its trajectory?
While running, a person dissipates about 0.600 J of mechanical energy per step per kilogram of body mass. If a 60.0-kg runner dissipates a power of 70.0 W during a race, how fast is the person
The direction of any vector A in three-dimensional space can be specified by giving the angles a, ß, and Ύ that the vector makes with the x, y, and z axes, respectively. If A = Axi + Ayj + Azk,
A 4.00-kg particle moves along the x axis. Its position varies with time according to x = t + 2.0t3, where x is in meters and t is in seconds. Find (a) The kinetic energy at any time t, (b) The
The spring constant of an automotive suspension spring increases with increasing load due to a spring coil that is widest at the bottom, smoothly tapering to a smaller diameter near the top. The
A bead at the bottom of a bowl is one example of an object in a stable equilibrium position. When a physical system is displaced by an amount x from stable equilibrium, a restoring force acts on it,
A traveler at an airport takes an escalator up one floor, as in Figure P7.52. The moving staircase would itself carry him upward with vertical velocity component v between entry and exit points
A mechanic pushes a car of mass m, doing work W in making it accelerate from rest. Neglecting friction between car and road, (a) What is the final speed of the car? During this time, the car moves
A 5.00-kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 3.20 mm deep, what is the average force exerted by the plate on the ball during the impact?
A single constant force F acts on a particle of mass m. The particle starts at rest at t = 0. (a) Show that the instantaneous power delivered by the force at any time t is P = (F2/m) t. (b) If F
Two springs with negligible masses, one with spring constant k1 and the other with spring constant k2 are attached to the end stops of a level air track as in Figure P7.56. A glider attached to both
As the driver steps on the gas pedal, a car of mass 1 160 kg accelerates from rest. During the first few seconds of motion, the car’s acceleration increases with time according to the expression a
A particle is attached between two identical springs on a horizontal frictionless table. Both springs have spring constant k and are initially unstressed.(a) If the particle is pulled a distance x
A rocket body of mass M will fall out of the sky with terminal speed vT after its fuel is used up. What power output must the rocket engine produce if the rocket is to fly (a) At its terminal speed
Two constant forces act on a 5.00-kg object moving in the xy plane, as shown in Figure P7.60. Force F1 is 25.0 N at 35.0°, while F2 is 42.0 N at 150°. At time t = 0, the object is at the
A 200-g block is pressed against a spring of force constant1.40 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal.
When different weights are hung on a spring, the spring stretches to different lengths as shown in the following table. (a) Make a graph of the applied force versus the extension of the spring. By
The ball launcher in a pinball machine has a spring that has a force constant of 1.20 N/cm (Fig. P7.63). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If
A 0.400-kg particle slides around a horizontal track. The track has a smooth vertical outer wall forming a circle with a radius of 1.50 m. The particle is given an initial speed of 8.00 m/s. After
In diatomic molecules, the constituent atoms exert attractive forces on each other at large distances and repulsive forces at short distances. For many molecules, the Lennard-Jones law is a good
As it plows a parking lot, a snowplow pushes an ever-growing pile of snow in front of it. Suppose a car moving through the air is similarly modeled as a cylinder pushing a growing plug of air in
A particle moves along the x axis from x = 12.8 m to x = 23.7 m under the influence of a force F= 375/x3 +3.75x Where F is in newtons and x is in meters. Using numerical integration, determine the
A windmill, such as that in the opening photograph of this chapter, turns in response to a force of high-speed air resistance, R = ½ D/Av2. The power available is P = Rv = ½Dpur2v3, where v is the
More than 2300 years ago the Greek teacher Aristotle wrote the first book called Physics. Put into more precise terminology, this passage is from the end of its Section Eta: Let P be the power of an
Consider the block-spring-surface system in part. (a) At what position x of the block is its speed a maximum? (b) In the What If? Section of this example, we explored the effects of an increased
A force F applied to an object of mass m1 produces an acceleration of 3.00 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.00 m/s2. (a) What is the value of
The largest-caliber antiaircraft gun operated by the German air force during World War II was the 12.8-cm Flak 40. This weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What propulsive
A 3.00-kg object undergoes an acceleration given by a = (2.00i + 5.00j) m/s2. Find the resultant force acting on it and the magnitude of the resultant force.
The gravitational force on a baseball is ─Fgj. A pitcher throws the baseball with velocity vi by uniformly accelerating it straight forward horizontally for a time interval Δt = t ─
To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a
The average speed of a nitrogen molecule in air is about 6.70 x 102 m/s, and its mass is 4.68 x 10─26 kg. (a) If it takes 3.00 x 10─13 s for a nitrogen molecule to hit a wall and
An electron of mass 9.11 x 10─31 kg has an initial speed of 3.00 x 105 m/s. It travels in a straight line, and its speed increases to 7.00 x 105 m/s in a distance of 5.00 cm. assuming its
A woman weighs 120 lb. Determine (a) her weight in newtons (N) and (b) her mass in kilograms (kg).
If a man weighs 900 N on the Earth, what would he weigh on Jupiter, where the acceleration due to gravity is 25.9 m/s2?
The distinction between mass and weight was discovered after Jean Richer transported pendulum clocks from Paris to French Guyana in 1671. He found that they ran slower there quite systematically. The
Two forces F1 and F2 act on a 5.00-kg object. If F1 = 20.0 N and F2 = 15.0 N, find the accelerations in (a) and (b) of Figure P5.11.
Besides its weight, a 2.80-kg object is subjected to one other constant force. The object starts from rest and in 1.20 s experiences a displacement of (4.20i ─ 3.30j) m, where the direction of
You stand on the seat of a chair and then hop off. (a) During the time you are in flight down to the floor, the Earth is lurching up toward you with an acceleration of what order of magnitude? In
Three forces acting on an object are given by F1 = (─2.00i + 2.00j) N, F2 = (5.00i ─ 3.00j) N, and F3 = (─45.0i) N. The object experiences an acceleration of magnitude 3.75 m/s2.
A 15.0-lb block rests on the floor. (a) What force does the floor exert on the block? (b) If a rope is tied to the block and run vertically over a pulley, and the other end is attached to a
A 3.00-kg object is moving in a plane, with its x and y coordinates given by x = 5t2 ─ 1 and y = 3t3 + 2, where x and y are in meters and t is in seconds. Find the magnitude of the net force
The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a free-body diagram of the bird. How much
A bag of cement of weight 325 N hangs from three wires as suggested in Figure P5.18. Two of the wires make angles θ1 = 60.0° and θ1 = 25.0° with the horizontal. If the system is
A bag of cement of weight Fg hangs from three wires as shown in Figure P5.18. Two of the wires make angles θ1 and θ2 with the horizontal. If the system is in equilibrium, show that the
You are a judge in a children€™s kite-flying contest, and two children will win prizes for the kites that pull most strongly and least strongly on their strings. To measure string tensions,
The systems shown in Figure P5.21 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? (Neglect the masses of the pulleys and strings, and assume the incline in part
Draw a free-body diagram of a block which slides down a frictionless plane having an inclination of θ = 15.0° (Fig. P5.22). The block starts from rest at the top and the length of the
A 1.00-kg object is observed to have an acceleration of 10.0 m/s2 in a direction 30.0° north of east (Fig. P5.23). The force F2 acting on the object has a magnitude of 5.00 N and is directed
A 5.00-kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 9.00-kg object, as in Figure P5.24. Draw free-body
A block is given an initial velocity of 5.00 m/s up a frictionless 20.0° incline (Fig. P5.22). How far up the incline does the block slide before coming to rest?
Two objects are connected by a light string that passes over a frictionless pulley, as in Figure P5.26. Draw free-body diagrams of both objects. If the incline is frictionless and ifm1 = 2.00 kg, m2
A tow truck pulls a car that is stuck in the mud, with a force of 2 500 N as in Fig. P5.27.The tow cable is under tension and therefore pulls downward and to the left on the pin at its upper end. The
Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine, as in Figure 5.14a. Determine (a) The tension
In Figure P5.29, the man and the platform together weigh 950 N. The pulley can be modeled as frictionless. Determine how hard the man has to pull on the rope to lift him steadily upward above the
In the Atwood machine shown in Figure 5.14a, m1 = 2.00 kg and m2 = 7.00 kg. The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not
In the system shown in Figure P5.31, a horizontal force Fx acts on the 8.00-kg object. The horizontal surface is frictionless. (a) For what values of Fx does the 2.00-kg object accelerate upward?
A frictionless plane is 10.0 m long and inclined at 35.0°. A sled starts at the bottom with an initial speed of 5.00 m/s up the incline. When it reaches the point at which it momentarily stops, a
A 72.0-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.20 m/s in 0.800 s. It travels with this constant speed for the next
An object of mass m1 on a frictionless horizontal table is connected to an object of mass m2 through a very light pulley P1 and a light fixed pulley P2 as shown in Figure P5.34.(a) If a1 and a2 are
The person in Figure P5.35 weighs 170 lb. As seen from the front, each light crutch makes an angle of 22.0° with the vertical. Half of the person€™s weight is supported by the crutches.
A 25.0-kg block is initially at rest on a horizontal surface. A horizontal force of 75.0 N is required to set the block in motion. After it is in motion, a horizontal force of 60.0 N is required to
A car is traveling at 50.0 mi/h on a horizontal highway. (a) If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will
Before 1960 it was believed that the maximum attainable coefficient of static friction for an automobile tire was less than 1. Then, about 1962, three companies independently developed racing tires
To meet a U.S. Postal Service requirement, footwear must have a coefficient of static friction of 0.5 or more on a specified tile surface. A typical athletic shoe has a coefficient of 0.800. In an
strap at an angle θ above the horizontal in Figure. She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. Draw a free-body diagram of the suitcase.(a)
A 3.00-kg block starts from rest at the top of a 30.0° incline and slides a distance of 2.00 m down the incline in 1.50 s. Find (a) The magnitude of the acceleration of the block, (b) The
A Chevrolet Corvette convertible can brake to a stop from a speed of 60.0 mi/h in a distance of 123 ft on a level roadway. What is its stopping distance on a roadway sloping downward at an angle of
A 9.00-kg hanging weight is connected by a string over a pulley to a 5.00-kg block that is sliding on a flat table (Fig.P5.24). If the coefficient of kinetic friction is 0.200, find the tension in
Three objects are connected on the table as shown in Figure P5.44. The table is rough and has a coefficient of kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00 kg, as
Two blocks connected by a rope of negligible mass are being dragged by a horizontal force F (Fig. P5.45). Suppose that F = 68.0 N, m1 = 12.0 kg, m2 = 18.0 kg, and the coefficient of kinetic friction
A block of mass 3.00 kg is pushed up against a wall by a force P that makes a 50.0° angle with the horizontal as shown in Figure P5.46. The coefficient of static friction between the block and
You and your friend go sledding. Out of curiosity, you measure the constant angle θ that the snow-covered slope makes with the horizontal. Next, you use the following method to determine the
The board sandwiched between two other boards in Figure P5.48 weighs 95.5 N. If the coefficient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assume
A block weighing 75.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied to the object at 40.0° to the horizontal, pushing it upward on the plane. The coefficients of
One side of the roof of a building slopes up at 37.0°. A student throws a Frisbee onto the roof. It strikes with a speed of 15.0 m/s and does not bounce, but slides straight up the incline. The
An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P5.51), Pat pulls on the
A time-dependent force, F = (8.00i ─ 4.00tj) N, where t is in seconds, is exerted on a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s?
To prevent a box from sliding down an inclined plane, student A pushes on the box in the direction parallel to the incline, just hard enough to hold the box stationary. In an identical situation
Three blocks are in contact with each other on a frictionless, horizontal surface, as in Figure P5.54. A horizontal force F is applied to m1. Take m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00 kg, and F =
An object of mass M is held in place by an applied force F and a pulley system as shown in Figure P5.55. The pulleys are mass less and frictionless. Find (a) the tension in each section of rope, T1,

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