Consider a system of two particles in the xy plane: m 1 = 2.00 kg is at the location r → 1 = ( 1.00 i ^ + 2.00 j ^ ) m and has a velocity of ( 3.00 i ^ + 0.500 j ^ ) m / s ; m 2 = 3.00 kg is at r → 2 = ( − 4.00 i ^ + 3.00 j ^ ) m and has velocity ( 3.00 i ^ + 2.00 j ^ ) m / s . (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Consider a system of two particles in the xy plane: m 1 = 2.00 kg is at the location r → 1 = ( 1.00 i ^ + 2.00 j ^ ) m and has a velocity of ( 3.00 i ^ + 0.500 j ^ ) m / s ; m 2 = 3.00 kg is at r → 2 = ( − 4.00 i ^ + 3.00 j ^ ) m and has velocity ( 3.00 i ^ + 2.00 j ^ ) m / s . (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Solution Summary: The author illustrates the position and velocity vectors of the two particles in x-y plane.
Consider a system of two particles in the xy plane: m1 = 2.00 kg is at the location
r
→
1
=
(
1.00
i
^
+
2.00
j
^
)
m
and has a velocity of
(
3.00
i
^
+
0.500
j
^
)
m
/
s
; m2 = 3.00 kg is at
r
→
2
=
(
−
4.00
i
^
+
3.00
j
^
)
m
and has velocity
(
3.00
i
^
+
2.00
j
^
)
m
/
s
. (a) Plot these particles on a grid or graph paper. Draw their position vectors and show their velocities. (b) Find the position of the center of mass of the system and mark it on the grid. (c) Determine the velocity of the center of mass and also show it on the diagram. (d) What is the total linear momentum of the system?
Two particles are moving in the x-y plane. Particle #1 has a mass m, = 6.40 kg and is located (at any time) by the position vector r, (t) = [0.300 m + (2.00 m/s?)t?jî + 0.200 mj. Particle #2 has a mass
m, = 9.00 kg and is located (at any time) by the position vector r,(t) = 0.100 mî + [0.300 m + (0.500 m/s)t + (1.50 m/s?)t?jj. Determine the following at the time t = 1.00 s. (Express your answers in
vector form.)
(a) location of the center of mass
r(t = 1.00 s) =
m
(b) velocity of the center of mass
Vem (t = 1.00 s) =
m/s
v
(c) acceleration of the center of mass
a(t = 1.00 s) =
m/s?
A small ball of mass mb = 0.050 kg is projected into a pendulum of mass Mp = 0.200 kg in a ballistic pendulum
experiment. How fast does the ball need to go in order to get the pendulum to swing up to a height of h = 0.25 m abov
its original position?
O 11.1 m/s
0.553 m/s
2.21 m/s
0.111 m/s
Consider a system of two particles in the xy-plane.
For the first particle,
Its mass is m₁ = 1.30 kg
Its position is 7¹₁ = (1.202 + 2.203) m
Its velocity is ₁ = (2.2002 + 0.100)) m/s
For the second particle,
Its mass is m₂ = 2.90 kg
Its position is 7¹2 = (-3.60% - 2.403) m
Its velocity is v₂ = (2.2001 - 2.000)) m/s
a. Find the position of the center of mass of the system.
7CM =
im+m
b. Determine the velocity of the center of mass.
UCM = 2 m/s + m/s
c. What is the total linear momentum of the system?
Pr =
kg-m/s + kg-m/s
Chapter 9 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.