Physics 2130 06

Two particles of masses m1m1m_1 and m2m2m_2 (m1<m2) are located 10 meters apart. Where is the center of mass of the system located?

more than 5 meters but less than 10 meters from the particle of mass m1

Impulse is

the area under the force-versus-time curve

For the system of particles described in the Part B, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right.

xcm =1.33L

What is the x coordinate xcmxcmx_cm of the center of mass of the system described in Part D?

1/3L From the symmetry of the situation, you can see that the x and y coordinates of the center of mass are the same.

Let us now consider an extended object. A wire is bent at its midpoint through a right angle as shown in the figure. Which arrow best shows the location of the center of mass of the system? Do not calculate. (Figure 5)

3 For an extended object, the center of mass does not have to be within the object itself. This wire is one example; one can think of many others including bagels. The exact location of the center of mass can be found using the symmetry approach: It is located halfway between the midpoints of the two straight segments of the wire (can you see why?).

Let us now consider a two-dimensional case. The system includes three particles of equal mass M located at the vertices of an isosceles triangle as shown in the figure. Which arrow best shows the location of the center of mass of the system? Do not calculate.

Arrow 4

Is the center of mass of the dumbbell in (Figure 1) at point a, b, or c? Explain.

As suggested by the figure, the larger sphere is more massive than the smaller sphere. If we suspend the dumbbell from its center of gravity, the counterclockwise torque due to the large sphere must be equal to the clockwise torque due to the small sphere. Since torque is the product of force and its moment arm, the center of gravity should be closer to the large sphere This occurs at point a.

A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. After the force is removed at t = 1 s, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart?

Because both carts start from rest, the change in momentum of each cart equals its final momentum. According to the momentum principle, the change in momentum of an object equals the impulse, which depends on the net force applied and the force action time Because equal forces are exerted over equal times and impulse is independent of the object's mass, the change in the momentum, as well as the final momentum of the plastic cart is equal to that of the lead cart.

Rank the automobiles based on the magnitude of the force needed to stop them, from largest to smallest.

The correct ranking cannot be determined The more momentum an object has, the more impulse is needed to stop it. However, this impulse can be provided via a large force acting over a short time interval or a relatively small force acting over a relatively long time interval. If you are driving down the highway at 55 mph, you can stop your car by either lightly pressing on the brakes and traveling a long time before stopping, or pressing more firmly on the brakes and stopping more quickly. In both cases, your braking system has applied the same amount of impulse to your car.

Which of the following best describes why you can analyze the interaction described in this problem using conservation of momentum?

The throwing action is quick enough that external forces may be ignored The quarterback-football system is not an isolated system because gravity, an external force, acts on the system. However, since the interaction between the objects (the quarterback and the ball) is very short, this external force can be ignored, and conservation of momentum can be applied in the horizontal direction.

A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what happens to the coordinates of the center of mass of the system of buckets?

The x coordinate decreases; the y coordinate decreases.

Rank in order, from largest to smallest, the momenta (px)a(px)a to (px)e(px)e of the objects in the figure(Figure 1)

b,(a,c,e),d

For the system of three particles shown, which have masses M, 2M, and 3M as indicated, where is the center of mass located?

between the particle of mass 2M and the particle of mass 3M

Momentum is conserved...

in an isolated system