Ap physics dynamics lesson 2.1 Center of mass

Center of mass

the single point in an object or system where its entire mass is concentrated

The formula for the position of the system's center of mass ( Xcm)

WRITE IT

Xcm= m1x1 + m2x2+ m3x3/ mtotal

Three 40g point masses are at the same points (7.07 cm, 0cm), (-7.07 cm, 0cm), and (0cm, -7.07 cm), and a 90g point mass is at (0cm, 7.07). What is the distance from the origin (0,0) to the center of mass?

1.68 cm

3 multiple choice options

A metallic sphere of mass 1 kg and radius 5cm is welded to the end B of a thin rod Ab of length 50 cm and mass 0.5 kg as shown in the picture. This rod with the sphere will balance horizontally on a knife's edge placed at x from the end of the rod if "x" is equal to:

45 cm

3 multiple choice options

mass 1 = 2kg and is located at x= 1m Mass m2 = 1 kg and is located at x = 2m mass m3 = 0.5 kg and is located at x= 2.5 m fine the center of mass of the system

1.5 cm

To weigh a fish a person hangs a tackle box of mass 3.5 kg and a cooler o mass 5kg from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod's length from the tackle box. What is the mass of the fish?

3 kg.

3 multiple choice options

A 5kg mass placed at the orgin and a 9kg mass placed at the x=2m where is the center of mass?

1.29 m

An 8kg mass is placed at y= 3m. Where should a 10 kg mass be placed along the y-axis so that the center of mass will be located at y= 4.5 m

y= 5.7 m

The positions of masse 4kg 6kg 7kg & 10 kg are (0,0) (4,0) (0,5) and (5,6) respectively determine the position of the center of mass of this system

(2.74, 3.519)

A 10 m long 4000 kg truck has its center of mass 4m behind the front of the truck Where should a 1400 load be placed so that the center of mass will be right in the middle of the truck

x = 7.86m

1st fact about the center of mass

If we don't have an external force acting on the system, the center of mass stays the same

No external force = constant velocity

Center of mass velocity

Vcm

Center of mass velocity formula

Vcm = m1v2+m2v2+ m32/ mass total

momentum

how much motion a system has

center of mass velocity =

system momentum

system momentum formula

p =total mass, total velocity/total mass

Velocity formula

Displacement/ time

practice

https://www.khanacademy.org/science/ap-college-physics-1/xf557a762645cccc5:linear-momentum/xf557a762645cccc5:center-of-mass/a/what-is-center-of-mass