Text Book (by Kleppner & Kolenkow) · Solutions to Selected Problems (of Kleppner & Kolenkow) [Question Numbers are marked on each of the pdf files.]. Solutions Manual to accompany AN INTRODUCTION TO MECHANICS 2nd edition Version 1 November KLEPPNER / KOLENKOW c Kleppner and. Solutions to Problems in Chapters 1 to 9 of the Kleppner and Kolenkow book Introduction to Mechanics - 1st Edition. Herminso Villarraga-Gómez. H. Villarraga -.

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Kleppner Kolenkow Solutions lesforgesdessalles.info (Distinguishing text: subatomic extemporization). Feel free to contact me with any questions or comments. Made with the. PDF | 5+ minutes read | This paper contains (handwritten) comprehensive Solutions to Problems in Chapters 1 to 9 of the Kleppner and Kolenkow book. Kleppner Daniel - Kolenkow Robert Solutions to mechanics 2th lesforgesdessalles.info - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free.

The length has kinetic energy K. This result is nearly independent of the number of men jumping. If Jupiter were not present, the radius of the asteroids orbit would be R. The coin is accelerating, so take torques about the center of mass. The 4th component gives.

In case b , therefore, the final speed of the flatcar could exceed u. From Example 4. Constructing a strong sail so extremely large and thin is beyond the limits of current technology. With reference to Example 4. Enclose the mirror with a hypothetical surface, as shown in the upper sketch. In steady conditions, the rate at which particles leave must equal the rate at which they arrive. The force Fhydrant on the hydrant due to the water is equal and opposite: Under steady conditions the rate of mass flow is constant, with an equal amount of mass passing through any horizontal plane per unit time, because water is essentially incompressible.

The momen- tum flux decreases with height, because the downward gravitational force is acting.

Let N be the number of droplets per m3 , and let md be the mass of each droplet. There are vN A droplets striking the bowl per second. Each droplet brings in momentum md v, and runs off with zero momentum, so the force F on the bowl is the change in momentum: The distance RS un of the Sun from the C. The upper sketch shows the forces on each bead: The lower sketch shows the forces on the ring: According to Eq.

Let xi be the maximum displacement of the block at the start. It starts from rest, so its kinetic energy is 0. If there is no friction, the block returns to xi after one complete cycle, and the mechanical energy is conserved.

Note that the lump transfers no horizontal momentum to M. Because the amplitude is unchanged, the mechanical energy is also unchanged.

The idealized sketch assumes that the scale has a very fast response. This problem could also be solved by calculating the im- pulse and the acceleration, but the energy method used here is more direct. How- ever, the result obtained is not entirely convincing. The assumption that the retard- ing force is constant is not realistic. For instance, if the compression acts more like a spring force, the peak force would be twice the average force.

Mechanical energy is conserved. The total gravitational potential energy is the sum of the potential energies of m with each mass M. Best practice is to work mainly in SI. The forces parallel to the surface are the component of gravity along the slope, the retarding force f , and the propelling force F.

The normal force on the snowmobile has no component along the slope, and is not shown in the sketches. The subscript u stands for up, and d for down. The power P delivered by the snow- mobile is Fv. At this point the speed is v0 , which carries the leaper an additional height h. To help understand what happens, consider a simple mechanistic model. The length has kinetic energy K. The kinetic energy of the rope is increasing at only half the rate of the first term in the expression for P.

The remainder is dissipated in the sudden acceleration of the rope from rest. Thinking of the rope as a chain, the speed of each link is changed abruptly, in an inelastic process that conserves momentum but not mechanical energy.

See the sketch for problem 5. The total potential energy is the sum of the potential energies due to each force. In the usual normal mode problem, the coupled equations of motion are solved for the frequencies, from which the relative amplitudes of the normal modes can be found. However, in a problem such as this that has a high degree of symmetry, the normal modes can be guessed, leading to the normal mode frequencies.

The corresponding normal mode frequencies are 1. As discussed in Example 6. As the sketch for mode B shows, masses 1 and 4 move together, and 2 and 3 also move together but in the opposite direction. All the modes conserve momentum, with the center of mass at rest. The time T n for the nth bounce is therefore! The time T f to finally come to rest is therefore! After the elastic bounce, M moves upward with p speed v0.

Here are two methods for finding the upward speed of the marble after it collides with the superball. To demonstrate the effect, it may be easier to use a coin instead of a marble, but a coin may experience greater air resistance.

Method 1: This method is algebraic, using the conservation laws for momentum and for mechanical energy. The top sketch shows the superball immediately after it has bounced off the floor. A gap greatly exaggerated in the sketch is shown between the marble, which is still moving downward with speed v0 , and the superball, which is moving upward with speed v0. The lower sketch shows the system immediately after the marble has collided with the superball.

The initial momentum just before the collision upper sketch is Pi , and the final momentum just after lower sketch is P f. Ki is the initial kinetic energy upper sketch , and K f is the kinetic energy just after the collision lower sketch. This method is nonalgebraic, and uses simple but sophisticated reasoning. To an observer on M moving upward , the marble just before the collision ap- pears to be approaching with speed 2v0.

Each car has mass M. The upper sketch is before the collision, and the lower sketch is after the collision. Both momentum P and mechanical energy kinetic energy K are conserved in the elastic collision. P has both x and y components. The collision is inelastic, so momentum P is conserved, but but mechanical energy E is not.

Squaring Eqs. After fission, the product 97 Sr and Xe nuclei move apart back-to- back, with equal and opposite momentum P. After fusion, the products have equal and opposite momentum P.

At threshold, the energy in the C system is just enough to form the products. If vn,C is moving parallel to V, the neutron will always be moving in the forward direction in L, and its energy is not restricted. The speed of the neutron in C is Vin this case, and it is moving antiparallel to V. Pushing the piston down does work on the gas, raising its temperature by increasing the average speed of the gas molecules.

Consider the situation when the walls are stationary. Then convert back to the lab frame by adding V.

To convert from C to L, add Vc to every velocity vector, as shown for mass m bottom sketch. To an observer on the drum, the sand appears to fly out radially. Angular momentum L about the pivot is conserved, because no external torques are acting on the system. The ring is then momentarily at rest, but it is not necessarily back to its initial position.

At tangential grazing, m is traveling at speed v and its trajectory is perpendicular to R. In this case, the package does not graze, but sails over the planet. Problem 7. Using Eqs. Note the exact analogy with linear acceleration under a constant force. Momentum p and mechanical energy E are not conserved, because external force is acting on m. Momentum is not conserved, because T dt , 0.

Mechanical energy is conserved, because the force T on m is perpendicular to v, and hence does no work. Both springs act to restore the rod toward equilibrium. At this point, the system is no longer stable, and the motion ceases to be harmonic. The second term is the angular momentum of a mass M concentrated at the end of the rod. The third term is the angular momentum of the disk.

The period is T , Eq. When the disk is mounted by a frictionless bearing, it cannot rotate and contributes no rotational angular momentum. The term 21 MR2 should then be omitted from Eq. Hence the angular momentum of the system is conserved. The new angular momentum L0 equals the initial L. Note that FV and F H do no work on the system, because the displacement is 0. Only the friction force f contributes. Let l0 be the initial length of the tape.

At the start, the object has only gravitational potential energy, and it gains kinetic energy as it rolls down the plane. Writing Eq. However, the solution requires that the Yo-yo be on the verge of slipping. Take angular momentum about any point on the alley, such as c in the sketch.

To keep the device from rotating, the hand must apply an opposite torque. Thus the angular momentum of the device is not conserved, so analyze the problem. The mass has gravitational potential energy and kinetic energy, and the cone has rota- tional kinetic energy.

The marble has gravitational potential energy E pot , translational kinetic energy Etrans , and rotational kinetic energy Erot. One way is to note the analogy between Eq. At the instant shown in the sketch, the pivot point is n. The horizontal displacement of the center of mass must be less than the displacement of n.

The motion is described most naturally as a combination of a uniform translation of the center of mass and a uniform rotation about the center of mass. Linear momentum, angular momentum, and mechanical energy are conserved. Linear momentum is also not conserved in the collision, because of the force exerted at the point of impact. The force at the point of impact exerts no torque about that point, but the wheel has angular momentum of translation.

Hence, angular momentum is conserved in the collision. However, it has angular momentum MvR from translation of the axis refer to Note 7.

Sketch a shows the system at the start, and at the instant just before the collision with the track. Mechanical energy E f is conserved following the collision, when the wheel is on the track. The wheel comes to rest when the spring is compressed to b0. Mechanical energy E f is con- served as the wheel moves off the track onto the smooth surface.

The velocity v changes with time because of the spring force, but the angular velocity remains constant, because there is no torque on the wheel about its center of mass. Thus the mechanical energy is equally divided between translation and rotation. As shown is sketch c , Lrot has re- versed its direction, so the total angular momentum is 0, and it remains 0 after the second collision. The second collision has dissipated all the remaining mechanical energy!

Because the wall and floor are frictionless, the force Fw exerted by the wall on the plank and the force F f exerted by the floor are normal to the surfaces, as shown in the lower sketch.

Let y0 be the initial height of the center of mass above the floor. We treated L as the angular momentum of a body with moment of inertia from the parallel axis theorem. From Secs. Without the flywheel, the torque due to friction f is balanced by the torque due to the unequal loading N1 and N2.

The flywheel thus needs to produce a counterclockwise torque on the car to balance the clockwise torque from f 0. If the car turns in the opposite direction, both the torque and the direction are reversed, so equal loading remains satisfied. This rotation is caused by precession of of its spin angular momentum due to the torque induced by the tilt.

The coin is accelerating, so take torques about the center of mass. The criterion is equivalent to being able to twirl a lariat vertically as well as horizontally. The hoop is vertical, so gravity exerts no torque. The blow by the stick is short, so the peak of force F is large; f can be neglected during the time of impact.

The spin- ning wheels increase the tilt angle by only about a degree, not a substantial effect. There is no applied torque, so the net rate of change is 0. As a Chegg Study subscriber, you can view available interactive solutions manuals for each of your classes for one low monthly price. Why buy extra books when you can get all the homework help you need in one place?

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