Q&A Hero

Q: The momentum of an object at a given instant is in the same direction as its: A) displacement B) velocity C) acceleration D) force E) Momentum is a scalar and does not have a direction.

Q: Momentum may be expressed in:A) kg/mB) gram.sC) N.sD) kg/(m.s)E) N/s

Q: A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg mass is attached to the other end. The masses are placed on a horizontal surface and the spring is compressed 10 cm. The spring is then released with the masses at rest and the masses oscillate. When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s. The mechanical energy that has been lost to this instant is: A) 0 J B) 0.31 J C) 0.61 J D) 0.81 J E) 1.2 J

Q: A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is: A) 3.0 m/s left B) 3.0 m/s, right C) 6.0 m/s, right D) 6.0 m/s, left E) 17 m/s, right

Q: The velocity of the center of mass of a system of particles changes as v= 4.5 t+ 2.4 t2+ 1.1 t3, where vis in meters per second. If the system starts from rest at t = 0, what is its position at t= 3.0 s? A) 7.1 m B) 21 m C) 40 m D) 49 m E) 64 m

Q: The acceleration of the center of mass of a system of particles changes as a= 4.5t + 2.4t2+ 1.1t3, where ais in m/s2. If the system starts from rest at t = 0, what is its velocity at t= 2.0 s? A) 8.0 m/s B) 14 m/s C) 20 m/s D) 27 m/s E) 34 m/s

Q: The velocity of the center of mass of a system of particles changes as v= 4.5 t+ 2.4 t2+ 1.1 t3, where vis in meters per second. If the system starts from rest at t = 0, what is its acceleration at t= 3.0 s? A) 7.1 m/s2 B) 14 m/s2 C) 20 m/s2 D) 49 m/s2 E) 65 m/s2

Q: The position of the center of mass of a system of particles moves as x= 4.5 t+ 2.4 t2+ 1.1t3, where xis in meters. If the system starts from rest at t = 0, what is its velocity at t= 3.0 s? A) 8.0 m/s B) 21 m/s C) 49 m/s D) 64 m/s E) 65 m/s

Q: At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the acceleration of the center of mass of the two-ball system is: A) 0.25g B) 0.50g C) 0.67 g D) 0.75 g E) 1.0 g

Q: A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30 m/s. Since the only forces on the blocks are the force of gravity, the normal force of the surface, and the force of the spring, we conclude that: A) the spring is compressed at the time of the observation B) the spring is not compressed at the time of observation C) the motion was started with the masses at rest D) the motion was started with at least one of masses moving E) the motion was started by compressing the spring

Q: At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass without colliding. At the end of 2.0 s the velocity of the center of mass of the two-ball system is: A) 11 m/s, down B) 11 m/s, up C) 15 m/s, down D) 15 m/s, up E) 20 m/s, down

Q: Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The center of mass of the two-block system is moving with the velocity of: A) 1.3 m/s in the same direction as A B) 1.3 m/s in the same direction as B C) 2.7 m/s in the same direction as A D) 1.0 m/s in the same direction as B E) 5.0 m/s in the same direction as A

Q: Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35 m/s, 45ï‚°above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0 s later, before either fragment has hit the ground? A) 1.2 m B) 20 m C) 31 m D) Can't tell because the velocities of the fragments are not given. E) Can't tell because the coordinates of the highest point are not given.

Q: A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest, the heavier object moves downward, and the lighter object moves upward with an acceleration of the same magnitude. Which of the following statements is true for the system consisting of the two objects? A) The center of mass remains at rest. B) The net external force is zero. C) The velocity of the center of mass is a constant. D) The acceleration of the center of mass is g, downward. E) None of the above statements are true.

Q: The center of mass of a system of particles obeys an equation similar to Newton's second law where: A) is the total internal force and mis the total mass of the system B) is the total internal force and mis the mass acting on the system C) is the total external force and mis the total mass of the system D) is the force of gravity and mis the mass of Earth E) is the force of gravity and mis the total mass of the system

Q: A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits there. Afterwards the canoe: A) is forward of its original position and moving forward B) is forward of its original position and moving backward C) is rearward of its original position and moving forward D) is rearward of its original position and moving backward E) is rearward of its original position and not moving

Q: The center of mass of a system of particles remains at the same place if: A) it is initially at rest and the external forces sum to zero B) it is initially at rest and the internal forces sum to zero C) the sum of the external forces is less than the maximum force of static friction D) no friction acts internally E) none of the above

Q: The center of mass of a system of particles has a constant velocity if: A) the forces exerted by the particles on each other sum to zero B) the external forces acting on particles of the system sum to zero C) the velocity of the center of mass is initially zero D) the particles are distributed symmetrically around the center of mass E) the center of mass is at the geometric center of the system

Q: A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third. Rank the three plates according to the xcoordinates of their centers of mass, from smallest to largest. A) 1, 2, 3 B) 1 and 2 tie, then 3 C) 1, then 2 and 3 tie D) 3, 2, 1 E) 1, 3, 2

Q: A thick uniform wire is bent into the shape of the letter "U" as shown. Which point indicates the location of the center of mass of this wire? A) A B) B C) C D) D E) E

Q: Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance? A) 4 m B) 5 m C) 6 m D) 10 m E) need to know the forces they exert

Q: A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20 m apart, on frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move: A) 1.0 m B) 3.3 m C) 10 m D) 12 m E) 17 m

Q: At the same instant that a 0.50-kg ball is dropped from 25 m above Earth, a second ball, with a mass of 0.25 kg, is thrown straight upward from Earth's surface with an initial speed of 15 m/s. They move along nearby lines and pass each other without colliding. At the end of 2.0 s the height above Earth's surface of the center of mass of the two-ball system is: A) 2.9 m B) 4.0 m C) 7.1 m D) 7.9 m E) 10.4 m

Q: The center of mass of Earth's atmosphere is: A) a little less than halfway between the Earth's surface and the outer boundary of the atmosphere B) near the surface of the Earth C) near the outer boundary of the atmosphere D) near the center of the Earth E) none of the above

Q: The center of mass of the system consisting of Earth, the Sun, and the planet Mars is: A) closer to the Earth than to either of the other bodies B) closer to the Sun than to either of the other bodies C) closer to Mars than to either of the other bodies D) at the geometric center of the triangle formed by the three bodies E) at the center of the line joining the Earth and Mars

Q: The center of mass of a uniform disk of radius Ris located: A) on the rim B) a distance R/2 from the center C) a distance R/3 from the center D) a distance 2R/3 from the center E) at the center

Q: The x andycoordinates in meters of the center of mass of the three-particle system shown below are: A) 0 m, 0 m B) 1.3 m, 1.7 m C) 1.4 m, 1.9 m D) 1.9 m, 2.5 m E) 1.4 m, 2.5 m

Q: Which one of the following statements is true? A) the center of mass of an object must lie within the object B) all the mass of an object is actually concentrated at its center of mass C) the center of mass of an object cannot move if there is zero net force on the object D) the center of mass of a cylinder must lie on its axis E) none of the above

Q: The energy of a system increases at a rate of 3.5 t+ 6.2 t2, in joules. What is the instantaneous power at t= 3.1 s? A) 3.5 W B) 6.2 W C) 16 W D) 42 W E) 70 W

Q: A stationary mass m= 1.3 kg is hanging from a spring of spring constant k= 1200 N/m. You raise the mass a distance of 10 cm above its equilibrium position in a time of 1.4 s. What was the average power expended? A) 0.93 W B) 4.3 W C) 5.2 W D) 8.6 W E) 10.2 W

Q: A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have: A) not changed B) decreased by 1.9 J C) decreased by 2.6 J D) increased by 1.9 J E) increased by 2.6 J

Q: A 5-kg projectile is fired over level ground with a velocity of 200 m/s at an angle of 25°above the horizontal. Just before it hits the ground its speed is 150 m/s. Over the entire trip the change in the thermal energy of the projectile and air is:A) +6300 JB) -6300 JC) +44,000 JD) -44,000 JE) 0 J

Q: A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is A) 19 m/s B) 35 m/s C) 40 m/s D) 45 m/s E) 53 m/s

Q: A block slides across a rough horizontal table top. The work done by friction changes: A) only the kinetic energy B) only the potential energy C) only the thermal energy D) only the kinetic and potential energies E) only the kinetic and thermal energies

Q: Objects A and B interact with each other via both conservative and nonconservative forces. Let KAand KBbe the kinetic energies, Ube the potential energy, and Eintbe the internal energy. If no external agent does work on the objects then: A) KA+ Uis conserved B) KA+ U+ Eintis conserved C) KA+ KB+ Eintis conserved D) KA+ KB+ Uis conserved E) KA+ KB+ U+ Eintis conserved

Q: Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest. A) The same for all cases B) 1, 2, 3 C) 1, then 2 and 3 tie D) 3, 1, 2 E) 2, 1, 3

Q: A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25°with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by:A) 0 JB) -9.8 JC) 9.8 JD) -18 JE) 18 J

Q: A stationary mass m= 1.3 kg is hanging from a spring of spring constant k= 1200 N/m. You raise the mass a distance of 10 cm above its equilibrium position. How much has the potential energy of the mass-spring system changed? A) 1.3 J B) 6.0 J C) 7.3 J D) 12 J E) 13 J

Q: The thermal energy of a system consisting of a thrown ball, Earth, and the air is most closely associated with: A) the gravitational interaction of the Earth and the ball B) the kinetic energy of the ball as a whole C) motions of the individual particles within the ball D) motions of individual particles within the ball and the air E) the kinetic energy of Earth as a whole

Q: The diagram shows a plot of the potential energy as a function of xfor a particle moving along the xaxis. The points of neutral equilibrium are: A) only a B) only b C) only c D) only d E) b and d

Q: The diagram shows a plot of the potential energy as a function of xfor a particle moving along the xaxis. The points of unstable equilibrium are: A) only a B) only b C) only c D) only d E) b and d

Q: The diagram shows a plot of the potential energy as a function of xfor a particle moving along the xaxis. The points of stable equilibrium are: A) only a B) only b C) only c D) only d E) b and d

Q: The potential energy of a particle moving along the xaxis is given byU(x) = (8.0 J/m2)x2+ (2.0 J/m4)x4.If the total mechanical energy is 9.0 J, the limits of motion are:A) -0.96 m; +0.96 mB) -2.2 m; +2.2 mC) -1.6 m; +1.6 mD) -0.96 m; +2.2 mE) -0.96 m; +1.6 m

Q: A particle is released from rest at the point x= aand moves along the xaxis subject to the potential energy function U(x) shown. The particle: A) moves to a point to the left of x= e, stops and remains at rest B) moves to the point x= e, then moves to the left C) moves to infinity at varying speed D) moves to x= bwhere it remains at rest E) moves to x= eand then to x= d, where it remains at rest

Q: A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is:A) B) 2g(h1- h2)C) (h1- h2)/2gD) E) (h1- h2)2/2g

Q: The potential energy of a 0.20-kg particle moving along the xaxis is given byU(x) =(8.0 J/m2)x2 + (2.0 J/m4)x4.When the particle is at x= 1.0 m it is traveling in the positive xdirection with a speed of 5.0 m/s. It next stops momentarily to turn around at x=A) 0 mB) -1.1 mC) 1.1 mD) -2.3 mE) 2.3 m

Q: In this graph of potential energy vs. x, the horizontal line represents the total mechanical energy of a particle. Approximately what is its kinetic energy at x= 15 m? A) 5 J B) 10 J C) 15 J D) 20 J E) 25 J

Q: The first graph shows the potential energy U(x) for a particle moving on the xaxis. Which of the following five graphs correctly gives the force Fexerted on the particle? A) I B) II C) III D) IV E) V

Q: As a particle moves along the xaxis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate xof the particle. Rank the labeled regions according to the magnitude of the force, least to greatest. A) AB, BC, CD B) AB, CD, BC C) BC, CD, AB D) BC, AB, CD E) CD, BC, AB

Q: Given a potential energy function U(x), the corresponding force is in the positive xdirection if: A) Uis positive B) Uis negative C) Uis an increasing function of x D) Uis a decreasing function of x E) it is impossible to obtain the direction of from U

Q: The potential energy for the interaction between the two atoms in a diatomic molecule is U= A/x12- B/x6, where Aand Bare constants and xis the interatomic distance. The magnitude of the force that one atom exerts on the other is:A) 12A/x13- 6B/x7B) -13A/x13+ 7B/x7C) -11A/x11+ 5B/x5D) 72A/x12- 72B/x6E) A/x13- B/x7

Q: The potential energy of a 0.20-kg particle moving along the x axis is given byU(x) = (8.0 J/m2)x2 -(2.0 J/m4)x4. When the particle is at x= 1.0 m the magnitude of its acceleration is:A) 0 m/s2B) -8 m/s2C) 8 m/s2D) -40 m/s2E) 40 m/s2

Q: The potential energy of a body of mass m is given by U= -mgx+ 1/2kx2. The corresponding force is:A) -mgx2/2 + kx3/6B) mgx2/2 - kx3/6C) -mg+ kx/2D) -mg+ kxE) mg- kx

Q: A particle moves along the xaxis under the influence of a stationary object. The net force on the particle, which is conservative, is given by F= (8N/m3)x3. If the potential energy is taken to be zero for x= 0 then the potential energy is given by:A) (2 J/m4)x4B) (-2 J/m4)x4C) (24 J/m2)x2D) (-24 J/m2)x2E) 5 J - (2 J/m4)x4

Q: The graphs below show the magnitude of the force on a particle as the particle moves along the positive xaxis from the origin to x= x1. The force is parallel to the xaxis and is conservative. The maximum magnitude F1has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive). A) 3, 1, 2 B) 1, 3, 2 C) 2, 3, 1 D) 3, 2, 1 E) 2, 1, 3

Q: A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball at the bottom of the circle is: A) B) C) D) E)

Q: A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3: A) its mechanical energy is a minimum B) the forces on it are balanced C) it is not accelerating D) its speed is a minimum E) it experiences a net upward force

Q: A small object of mass mstarts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R. What is the smallest value of ysuch that the object will slide without losing contact with the track? A) R/4 B) R/2 C) R D) 2R E) 0

Q: The string in the figure is 50 cm long. When the ball is released from rest, it swings along the dotted arc. How fast is it going at the lowest point in its swing? A) 2.0 m/s B) 2.2 m/s C) 3.1 m/s D) 4.4 m/s E) 6.0 m/s

Q: A small object of mass m, on the end of a light cord, is held horizontally at a distance rfrom a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing? A) mg/2 B) mg C) 2 mg D) 3 mg E) mgr

Q: A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is: A) 1.02 m/s B) 1.41 m/s C) 2.00 m/s D) 2.04 m/s E) 4.00 m/s

Q: A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to its unstretched potential energy, is: A) 300 J B) 710 J C) 850 J D) 7000 J E) 8400 J

Q: A block of mass mis initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of: A) B) (1/2)mv2 C) (1/4)mv2 D) mv2/4k E) (1/4)

Q: A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is: A) 0.6 cm B) 3 cm C) 5 cm D) 7 cm E) 8 cm

Q: A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. When the spring is 4.0 cm longer than its equilibrium length, the speed of the block is 0.50 m/s. The greatest speed of the block is: A) 0.32 m/s B) 0.55 m/s C) 0.71 m/s D) 0.87 m/s E) 0.93 m/s

Q: A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest speed of the block is: A) 0.15 m/s B) 0.24 m/s C) 0.49 m/s D) 0.69 m/s E) 1.46 m/s

Q: Which of the five graphs correctly shows the potential energy of a spring as a function of its elongation x? A) I B) II C) III D) IV E) V

Q: The long pendulum shown is drawn aside until the ball has risen 0.5 m. It is then given an initial speed of 3.0 m/s. The speed of the ball at its lowest position is: A) 0 m/s B) 0.89 m/s C) 3.1 m/s D) 3.7 m/s E) 4.3 m/s

Q: An ideal spring is used to fire a 15.0-g block horizontally. The spring has a spring constant of 20 N/m and is initially compressed by 7.0 cm. The kinetic energy of the block as it leaves the spring is:A) 0 JB) 2.5 x10-2JC) 4.9 x10-2JD) 9.8 x10-2JE) 1.4 J

Q: A simple pendulum consists of a 2.0 kg mass attached to a string. It is released from rest at X as shown. Its speed at the lowest point Y is: A) 1.9 m/s B) 3.7 m/s C) 4.4 m/s D) 6.0 m/s E) 36 m/s

Q: A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop in order to remain in contact with the loop? A) 1.9 m/s B) 3.8 m/s C) 5.4 m/s D) 15 m/s E) 29 m/s

Q: For a block of mass mto slide without friction up the rise of height hshown, it must have a minimum initial kinetic energy of: A) gh B) mgh C) gh/2 D) mgh/2 E) 2mgh

Q: A projectile of mass 0.50 kg is fired with an initial speed of 10 m/s at an angle of 60ï‚°above the horizontal. The potential energy of the projectile-Earth system when the projectile is at its highest point (relative to the potential energy when the projectile is at ground level) is: A) 25 J B) 18.75 J C) 12.5 J D) 6.25 J E) none of these

Q: An elevator is rising at constant speed. Consider the following statements: I. the upward cable force is constant II. the kinetic energy of the elevator is constant III. the gravitational potential energy of the Earth-elevator system is constant IV. the acceleration of the elevator is zero V. the mechanical energy of the Earth-elevator system is constant A) all five are true B) only II and V are true C) only IV and V are true D) all but III are true E) only I, II, and IV are true

Q: A 6.0-kg block is released from rest 80 m above the ground. When it has fallen 60 m its kinetic energy is approximately: A) 4700 J B) 3500 J C) 1200 J D) 120 J E) 60 J

Q: A 0.20-kg particle moves along the xaxis under the influence of a conservative force. The potential energy is given by U(x) = (8.0J/m2)x2+ (2.0J/m4)x4, where xis in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x= 1.0 m, its speed when it is at the origin is: A) 0 m/s B) 2.5 m/s C) 5.7 m/s D) 7.9 m/s E) 11 m/s

Q: The sum of the kinetic and potential energies of a system of objects is conserved: A) only when no external force acts on the objects B) only when the objects move along closed paths C) only when the work done by the resultant external force is zero D) always E) none of the above

Q: A ball is held at a height H above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy E of the Earth-ball system as a function of the altitude yof the ball? A) I B) II C) III D) IV E) V

Q: A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. The total mechanical energy is 0.12 J. The greatest extension of the spring from its equilibrium length is:A) 1.5x10-3mB) 3.0 x10-3mC) 0.039 mD) 0.055 mE) 18 m

Q: A force of 10 N holds an ideal spring with a 20-N/m spring constant in compression. The potential energy stored in the spring is: A) 0.5 J B) 2.5 J C) 5 J D) 10 J E) 200 J