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Consider a system of three particles moving in the xy plane. The masses and the components of their positions as functions of time are given by

m1 = 1.00 kgm2 = 2.00 kgm3 = 3.00 kg
x1 = (5 m/s2)t2 + 3 mx2 = 3 mx3 = (3 m/s)t
y1 = 0y2 = 4 m + (2 m/s)ty3 = (6 m/s2)t2

Determine the following:

1
Coordinates of the CM of the system after 2.00 s
2
Coordinates of the velocity of the CM of the system after 2.00 s
3
Coordinates of the acceleration of the CM of the system after 2.00 s
4
Coordinates of the net force on the system after 2.00 s

A 100-g ball moving at a speed of 40.0 m/s strikes a wall at an angle of 60.0° with respect to the normal. There is no change in the component of the velocity parallel to the wall and the ball leaves the wall with a speed of 38.0 m/s. The ball and wall are in contact for 0.100 s.

Determine the following:

5
Magnitude of the ball's initial momentum
6
Component of the ball's initial velocity perpendicular to the wall
7
Component of the ball's final velocity perpendicular to the wall
8
Angle with which the ball leaves the wall
9
Magnitude of the ball's final momentum
10
Magnitude of the impulse imparted to the ball
11
Magnitude of the average force exerted on the ball

m1 is released from rest and collides elastically with m2. The objects have the same mass, the horizontal surface is frictionless, the cord attached to m1 is 1.00 m long, and θ is 30.0°.<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/ch7_img1.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>

Determine the following:

12
Speed of m1 the instant before the collision
13
Speed of m1 after the collision
14
Speed of m2 after the collision

m1 and m2 are traveling as shown in the figure below. m1 slides down the ramp, overtaking and colliding elastically with m2. The surface is frictionless.

m1 = 400 g     h = 1.00 m
m2 = 200 g    μ = 0
v1i = v2i = 1.00 m/s
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/ch7_img2.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>

Determine the following:

15
Speed of m1 the instant before the collision
16
Speed of m1 after the collision
17
Speed of m2 after the collision

m1 and m2 travel toward each other before colliding inelastically and sticking together, as shown in the figure below. The surface is frictionless.

m1 = 400 g    v1i = +1.00 m/s
m2 = 200 g    v2i = -3.00 m/s
   μ = 0
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/ch7_img3.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>

Determine the following:

18
Velocity of m1 after the collision
19
Velocity of m2 after the collision

m1 is fired into m2 which is initially at rest on a rough surface. The collision is totally inelastic. The composite object (m1 + m2) travels 5.00 m across the surface before coming to rest.<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070524076/57990/ch7_img4.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>

Determine the following:

20
Speed of the composite object the instant after collision
21
Acceleration of the composite object as it slides
22
Frictional force decelerating the composite object
23
Coefficient of friction for the composite object on the rough surface







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