Questions and Answers of Classical Dynamics Of Particles

A particle of mass m travels in a hyperbolic orbit past a mass M, whose position is assumed to be fixed. The speed at infinity is v0, and the impact parameter is b (see Exercise 6).(a) Show that the
During a daring rescue, a helicopter rescue squad initially accelerates a little girl (mass 25.0 kg) vertically off the roof of a burning building. They do this by drop-ping a rope down to her, which
A 75.0-kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator is (a) At rest, (b) Moving up at a constant velocity of 2.00 m/s, and (c)
In Exercise 36, what if the elevator is accelerating down at 2.00 m/s? In exercise A 75.0-kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator
(a) When an object is on an inclined plane, the nor-mal force exerted by the inclined plane on the object is (1) less than, (2) equal to, (3) more than the weight of the object. Why? (b) For a 10-kg
The weight of a 500-kg object is 4900 N. (a) When the object is on a moving elevator, its measured weight could be (1) zero, (2) between zero and 4900 N, (3) more than 4900 N, (4) all of the
A net force of 4.0 N gives an object an acceleration of 10 m/s2. What is the mass of the object?
A boy pulls a box of mass 30 kg with a force of 25 N in the direction shown in Fig. 4.38.(a) Ignoring friction, what is the acceleration of the box? (b) What is the nor-mal force exerted on the box
A girl pushes a 25-kg lawn mower as shown in Fig. 4.39. If F = 30 N and Î¸ = 37°(a) What is the acceleration of the mower, and(b) What is the normal force exerted on the mower by the
A 3000-kg truck tows a 1500-kg car by a chain. If the net forward force on the truck by the ground is 3200 N, (a) What is the acceleration of the car, and (b) What is the tension in the connecting
A block of mass 25.0 kg slides down a frictionless surface inclined at 30°. To ensure that the block does not accelerate, what is the smallest force that you must exert on it and what is its
(a) An Olympic skier coasts down a slope with an angle of inclination of 37o. Neglecting friction, there is (are) (1), one, (2) two, (3) three force(s) acting on the skier. (b) What is the
A car coasts (engine off) up a 30o grade. If the speed of the car is 25 m/s at the bottom of the grade, what is the distance traveled by the car before it comes to rest?
Assuming ideal frictionless conditions for the apparatus shown in Fig. 4.40, what is the acceleration of the sys-tem if(a) m1 = 0.25 kg, m2 = 0.50 kg. and m3 = 0.25 kg.(b) m1 = 0.35 kg, m2 = 0.15 kg,
A rope is fixed at both ends on two trees and a bag is hung in the middle of the rope (causing the rope to sag vertically). (a) The tension in the rope depends on (1) only the tree separation, (2)
A 55-kg gymnast hangs vertically from a pair of parallel rings. (a) If the ropes supporting the rings are attached to the ceiling directly above, what is the tension in each rope? (b) If the ropes
A physicist’s car has a small lead weight suspended from a string attached to the interior ceiling. Starting from rest, after a fraction of a second the car accelerates at a steady rate for about
Consider a 2.0-kg ball and a 6.0-kg ball in free fall. (a) What is the net force acting on each? (b) What is the acceleration of each?
A 10-kg mass is suspended as shown in Fig. 4.41. What is the tension in the cord between points A and B?
Referring to Fig. 4.41, what are the tensions in all the cords?
At the end of most landing runways in airports, an extension of the runway is constructed using a special substance called formcrete. Formcrete can support the weight of cars, but crumbles under the
A rifle weighs 50.0 N and its barrel is 0.750 m long. It shoots a 25.0-g bullet, which leaves the barrel at a speed (muzzle velocity) of 300 m/s after being uniformly accelerated. What is the
A horizontal force of 40 N acting on a block on a frictionless, level surface produces an acceleration of 2.5 m/s2. A second block, with a mass of 4.0 kg, is dropped onto the first. What is the
The Atwood machine consists of two masses suspended from a fixed pulley, as shown in Fig. 4.42. It is named after the British scientist George Atwood (1746€“ 1807), who used it to study
An Atwood machine (see Fig. 4.42) has suspended masses of 0.25 kg and 0.20 kg. Under ideal conditions, what will be the acceleration of the smaller mass?
One mass, m1 = 0.215 kg, of an ideal Atwood machine (see Fig. 4.42) rests on the floor 1.10 m below the other mass, m2 = 0.255 kg,(a) If the masses are released from rest, how long does it take m2 to
Two blocks are connected by a light string and accelerated upward by a pulling force F. The mass of the upper block is 50.0 kg and that of the lower block is 100 kg. The upward acceleration of the
Two blocks on a level, frictionless table are in con-tact. The mass of the left block is 5.00 kg and the mass of the right block is 10.0 kg, and they accelerate to the left at 1.50 m/s2. A person on
A hockey puck with a weight of 0.50 lb is sliding freely across a section of very smooth (frictionless) horizontal ice. (a) When it is sliding freely, how does the upward force of the ice on the
In the frictionless apparatus shown in Fig. 4.43, m1 = 2.0 kg. What is m2 if both masses are at rest? How about if both masses are moving at constant velocity?
In the ideal setup shown in Fig. 4.43, m1 = 3.0 kg and m2 = 2.5 kg.(a) What is the acceleration of the masses? (b) What is the tension in the string?
A 20-kg box sits on a rough horizontal surface. When a horizontal force of 120 N is applied, the object accelerates at 1.0 m/s2. (a) If the applied force is doubled, the acceleration will (1)
The coefficients of static and kinetic friction between a 50.0-kg box and a horizontal surface are 0.500 and 0.400 respectively. (a) What is the acceleration of the object if a 250-N horizontal
In moving a 35.0-kg desk from one side of a classroom to the other, a professor finds that a horizontal force of 275 N is necessary to set the desk in motion, and a force of 195 N is necessary to
A 40-kg crate is at rest on a level surface. If the coefficient of static friction between the crate and the surface is 0.69, what horizontal force is required to get the crate moving?
A packing crate is placed on a inclined plane. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane if released from rest? Justify your
A 1500-kg automobile travels at 90 km/h along a straight concrete highway. Faced with an emergency situation, the driver jams on the brakes, and the car skids to a stop. What is the car’s stopping
A hockey player hits a puck with his stick, giving the puck an initial speed of 5.0 m/s. If the puck slows uniformly and comes to rest in a distance of 20 m, what is the coefficient of kinetic
A crate sits on a flat-bed truck that is traveling with a speed of 50 km/h on a straight, level road. If the coefficient of static friction between the crate and the truck bed is 0.30, in how short a
A 5.0-kg block at rest on a frictionless surface is acted on by forces F1 = 5.5 and F2 = 3.5 N as illustrated in Fig. 4.33. What additional force will keep the block at rest?
A block is projected with a speed of 2.5 m/s on a horizontal surface. If the block comes to rest in 1.5 m, what is the coefficient of kinetic friction between the block and the surface?
A block is projected with a speed of 3.0 m/s on a horizontal surface. If the coefficient of kinetic friction between the block and the surface is 0.60, how far does the block slide before coming to
A person has a choice while trying to push a crate across a horizontal pad of concrete: push it at a down-ward angle of 30o, or pull it at an upward angle of 30o. (a) Which choice is most likely to
Suppose the slope conditions for the skier shown in Fig. 4.44 are such that the skier travels at a constant velocity. From the photo, could you find the coefficient of kinetic friction between the
A 5.0-kg wooden block is placed on an adjustable wooden inclined plane. (a) What is the angle of incline above which the block will start to slide down the plane? (b) At what angle of incline will
A block that has a mass of 2.0 kg and is 10 cm wide on each side just begins to slide down an inclined plane with a angle of incline (Fig. 4.45). Another block of the same height and same material
In the apparatus shown in Fig. 4.46, m1 = 10 kg and the coefficients of static and kinetic friction between m1 and the table are 0.60 and 0.40, respectively.(a) What mass of m2 will just barely set
In loading a fish delivery truck, a person pushes a block of ice up a 20o incline at constant speed. The push is 150 N in magnitude and parallel to the incline. The block has a mass of 35.0 kg. (a)
An object (mass 3.0 kg) slides upward on a vertical wall at constant velocity when a force F of 60 N acts on it at an angle of to the horizontal. (a) Draw the free-body diagram of the object. (b)
In the apparatus shown in Fig. 4.43, and the coefficients of static and kinetic friction between m1 and the inclined plane are 0.30 and 0.20, respectively.(a) What is m2 if both masses are at rest?
(a) You are told that an object has zero acceleration. Which of the following is true: (1) The object is at rest; (2) the object is moving with constant velocity; (3) either (1) or (2) is possible;
For the apparatus shown in Fig. 4.40, what is the minimum value of the coefficient of static friction between the block (m3) and the table that would keep the system at rest if m1 = 0.25 kg, m2 =
If the coefficient of kinetic friction between the block and the table in Fig. 4.40 is 0.560, and m1 = 0.150 kg and m2 = 0.250 kg,(a) What should m3 be if the system is to move with a constant speed?
One block (A, mass 2.00 kg) rests atop another (B, mass 5.00 kg) on a horizontal surface. The surface is a powered walkway accelerating to the right at 2.50 m/s2. B does not slip on the walkway
Two blocks (A and B) remain stuck together as they are pulled to the right by a force F = 200 N (Fig. 4.47). B is on a rough horizontal tabletop (coefficient of kinetic friction of 0.800).(a) What is
To haul a boat out of the water for the winter, a worker at the storage facility uses a wide strap with cables operating at the same angle (measured from the horizontal) on either side of the boat
You are in charge of an accident reconstruction case for the local police department. In order to determine car speeds, skid mark lengths are measured. To determine the coefficient of kinetic
Compare two different situations in which a ball and hard surface exert forces on one another. First, a putty ball is placed gently on the floor and left at rest. Then it is dropped from a height of
A hockey puck impacts a goalie’s plastic mask horizontally at and rebounds horizontally off the mask at 47 mi/h. If the puck has a mass of 170 g and it is in contact with the mask for 25 ms, (a)
A 2.50-kg block is placed on a rough surface inclined at 30o. The block is propelled and launched at a speed of down the incline and comes to rest after sliding 1.10 m. (a) Draw the free-body
A fish weighing 25 lb is caught and hauled onto the boat. (a) Compare the tension in the fishing line when the fish is brought up vertically at a constant speed to the tension when the fish is held
(a) If an object is at rest, there must be no forces acting on it. Is this statement correct? Explain. (b) If the net force on an object is zero, can you conclude that the object is at rest? Explain.
In general, this chapter has considered forces that are applied to objects of constant mass. What would be the situation if mass were added to or lost from a system while a constant force was being
The engines of most rockets produce a constant thrust (forward force). However, when a rocket is fired, its acceleration increases with time as the engine continues to operate. Is this situation a
In football, good wide receivers usually have €œsoft€ hands for catching balls (Fig. 4.30). How would you interpret this description on the basis of Newton€™s second
Draw the free-body diagram for a person sitting in the seat of an aircraft (a) That is accelerating down the run-way for takeoff, and (b) After takeoff at a angle to the ground.
A person pushes perpendicularly on a block of wood that has been placed against a wall. Draw a free-body diagram of the block and identify the reaction forces to all the forces on the block.
A person on a bathroom scale (not the digital type) stands on the scale with his arms at his side. He then quickly raises his arms over his head, and notices that the scale reading increases as he
Identify the direction of the friction force in the following cases: (a) A book sitting on a table; (b) A box sliding on a horizontal surface; (c) A car making a turn on a flat road; (d) The
When on a jet airliner that is taking off, you feel that you are being “pushed” back into the seat. Use Newton’s first law to explain why.
Shown in Fig. 4.31 are the front and rear wings of an Indy racing car.These wings generate down force, which is the vertical downward force produced by the air moving over the car. Why is such a down
(a) We commonly say that friction opposes motion. Yet when we walk, the frictional force is in the direction of our motion (Fig. 4.17). Is there an inconsistency in terms of Newton€™s
Why are drag- racing tires wide and smooth, whereas passenger- car tires are narrower and have tread (Fig. 4.32)? Are there frictional and/ or safety considerations? Does this difference between the
How could you approximately determine the coefficient of kinetic friction between your shoes and a fairly smooth floor?
Consider an air-bubble level that is sitting on a horizontal surface (Fig. 4.27). Initially, the air bubble is in the middle of the horizontal glass tube.(a) If the level is pushed and a force is
As a follow-up to Conceptual Question 4, consider a child holding a helium balloon in a closed car at rest. What would the child observe when the car (a) Accelerates from rest (b) Brakes to a stop?
The following is an old trick (Fig. 4.28). If a tablecloth is yanked out very quickly, the dishes on it will barely move. Why?
Another old one: Referring to Fig. 4.29,(a) How would you pull to get the upper string to break?(b) How would you pull to get the lower string to break?
A student weighing 600 N crouches on a scale and suddenly springs vertically upward. Will the scale read more or less than 600 N just before the student leaves the scale?
Which has more inertia, 20 cm3 of water or 10 cm3 of aluminum, and how many times more?
A 1.5-kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces at 37o above the +x-axis, F2 = 2.5 N in the + x-direction, F3 = 3.5 N at 45o below the – x-axis, and
Three horizontal forces (the only horizontal ones) act on a box sitting on a floor. One (call it F1) acts due east and has a magnitude of 150 lb. A second force (call it F2) has an easterly component
A 6.0-N net force is applied to a 1.5-kg mass. What is the object’s acceleration?
A force acts on a 1.5-kg, mass, giving it an acceleration of 3.0 m/s2. (a) If the same force acts on a 2.5-kg mass, what acceleration would be produced? (b) What is the magnitude of the force?
A 6.0-kg object is brought to the Moon, where the acceleration due to gravity is only one-sixth of that on the Earth. (a) The mass of the object on the Moon is (1) zero, (2) 1.0 kg, (3) 6.0 kg, (4)
A gun is fired and a 50-g bullet is accelerated to a muzzle speed of 100 m/s. If the length of the gun barrel is 0.90 m, what is the magnitude of the accelerating force? (Assume the acceleration to
Fig. 4.34 shows a product label.(a) This label is correct (1) on the Earth; (2) on the Moon, where the acceleration due to gravity is only one-sixth of that on the Earth; (3) in deep space, where
In a college homecoming competition, eighteen students lift a sports car. While holding the car off the ground, each student exerts an upward force of 400 N. (a) What is the mass of the car in
(a) A horizontal force acts on an object on a frictionless horizontal surface. If the force is halved and the mass of the object is doubled, the acceleration will be (1) four times, (2) two times,
Two forces act on a 5.0-kg object sitting on a friction-less horizontal surface. One force is 30 N in the +x-direction, and the other is 35 N in the –x-direction. What is the acceleration of the
A force of 50 N acts on a mass m1, giving it an acceleration of 4.0 m/s2. The same force acts on a mass m2 and produces an acceleration of 12 m/s2. What acceleration will this force produce if the
A student weighing 800 N crouches on a scale and suddenly springs vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration
The engine of a 1.0-kg toy plane exerts a 15-N for-ward force. If the air exerts an 8.0-N resistive force on the plane, what is the magnitude of the acceleration of the plane?
When a horizontal force of 300 N is applied to a 75.0-kg box, the box slides on a level floor, opposed by a force of kinetic friction of 120 N. What is the magnitude of the acceleration of the box?
A rocket is far away from all planets and stars, so gravity is not a consideration. It is using its rocket engines to accelerate upward with an acceleration a = 9.80 m/s2. On the floor of the main
An object (mass 10.0 kg) slides upward on a slippery vertical wall. A force F of 60 N acts at an angle of as shown in Fig. 4.36.(a) Determine the normal force exerted on the object by the wall.(b)
In an emergency stop to avoid an accident, a shoulder-strap seatbelt holds a 60-kg passenger in place. If the car was initially traveling at and came to a stop in 5.5 s along a straight, level road,
A student is assigned the task of measuring the startup acceleration of a large RV (recreational vehicle) using an iron ball suspended from the ceiling by a long string. In accelerating from rest,
A force of 10 N acts on two blocks on a frictionless surface (Fig. 4.37).(a) What is the acceleration of the system?(b) What force does block A exert on block B?(c) What force does block B exert on
A 2.0-kg object has an acceleration of 1.5 m/s2 at 30o above the – x-axis. Write the force vector producing this acceleration in component form.

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