A system consists of three particles with these masses and velocities: mass 3.0 kg, moving north at 3.0 m/s; mass 4.0 kg, moving sooth at 5.0 m/s; and mass 7.0 kg, moving north at 2.0 m/s. What is the total momentum of the system?

A ball of mass 5.0 kg moving with a speed of 2.0 m/s in the + x-direction hits a wall and bounces back with the same speed in the -x-direction. What is the change of momentum of the ball?

Figure shows three particles of the same mass and the same constant speed moving as indicated by the velocity vectors. Points a, b, c, and d form a square, with point e at the center. Rank the points according to the magnitude of the net angular momentum of the three-particle system when measured about the points, greatest first.

What is the momentum of an automobile (weight=9800 N) when it is moving at 35 m/s to the south?

Particle A has a mass of 5.0 g and particle B has a mass of 1.0 g. Particle A is located at the origin and particle B is at the point (x, y)=(25 cm, 0). What is the location of the CM?

The system of three particles has the indicated particle masses, velocities, and external forces. Determine $\overline{\mathbf{r}}, \dot{\overline{\mathbf{r}}}, \ddot{\overline{\mathbf{r}}}, T, \mathbf{H}_O$, and $\dot{\mathbf{H}}_O$ for this system.

A 3.0 kg object is initially moving northward at 15 m/s. Then a force of 15 N, toward the east, acts on if for 4.0 s. (a) At the end of the 4.0 s, what is the objects final velocity? (b) What is the change in momentum during the 4.0 s?

Determine the angular momentum ${H}_{O}$ of each of the two particles about point O .

Consider a system of five particles, inside a container where the allowed energy levels are nondegenerate and evenly spaced. For instance, the particles could be trapped in a one-dimensional harmonic oscillator potential. In this problem you will consider the allowed states for this system, depending on whether the particles are identical fermions, identical bosons, or distinguishable particles. (a) Describe the ground state of this system, for each of these three cases. (b) Suppose that the system has one unit of energy (above the ground state). Describe the allowed states of the system, for each of the three cases. How many possible system states are there in each case? (c) Repeat part (b) for two units of energy and for three units of energy. (d) Suppose that the temperature of this system is low, so that the total energy is low (though not necessarily zero). In what way will the behavior of the bosonic system differ from that of the system of distinguishable particles? Discuss.

Evaluate the integral. Wherever they appear, $\alpha$ and $\beta$ are positive numbers. $\int_{-\infty}^{\infty} \frac{\cos (\beta x)}{\left(x^{2}+\alpha^{2}\right)^{2}} d x$

A pole-vaulter of mass 60.0 kg vaults to a height of 6.0 m before dropping to thick padding placed below to cushion her fall. (a) Find the speed with which she lands. (b) If the padding brings her to a stop in a time of 0.50 s, what is the average force on her body due to the padding during that time interval?

Blocks with masses of 1.0 kg, 2.0 kg, and 3.0 kg are lined up in a row on a frictionless table. All three are puched forward by a 12 N force applied to the 1.0 kg block. How much force does the 2.0 kg block exert on (a) the 3.0 kg block and (b) the 1.0 kg block?

A system consists of 3 particles with these masses and velocities: mass 3 kg moving north at 3 m/s; mass 4 kg moving south at 4.8 m/s; and mass 7 kg moving north at 2 m/s. What is the total momentum of the system? Take north as the positive axis. Enter a positive answer if the total momentum is due north and a negative answer if the momentum is due south.

Using the scale $\frac{1}{4}$ in. $=2 \overline{0} \mathrm{mi}$, find the length of the vector that represents the displacement.

Displacement $75 \mathrm{mi}$ at $25^{\circ}$ west of north $\qquad$length $=\underline{\qquad}$ in.