Which of these is largest? A. asteroids B. comets C. meteoroids D. planets
2 answers:
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Answer:
(5/3,-5/6) or (1.67, -0.83)
Explanation:
the center if there are 4 bricks is the point 0,0 or intersection of the two arrow.
if we remove one on the top left, with the center of the mass in (-5,2.5), the the new coordinates of the center of mass can be found like this
x = A1 x1 - A2 x2 / (A1 - A2)
x = new coordinate of the system
A1 is the Area of 4 bricks = 20 x 10 = 200 cm²
A2 is the Area of 1 brick we remove, the top left = 10 x 5 = 50 cm²
x1 = the x coordinate of the center of mass when there are 4 bricks, x = 0
x2 = the x coordinate of the center of mass of the remove brick, x = -5
x = (200 . 0) - (50 . (-5))/(200 - 50)
x = - (-250) / 150
x = 250/150 = 5/3 = 1.67 cm
we can find the value y of the new coordinate, the same way we find x
y = A1 y1 - A2 y2 / (A1 - A2)
y = (200 . 0) - (50 . 2.5) / (200-50)
y = - 125/150
y = -5/6 = -0.83 cm
Speed of the block at the bottom of the incline: 5.42 m/s
The first part of the problem can be solved by using the law of conservation of energy. Since the ramp is frictionless, the initial gravitational potential energy of the block at the top of the ramp is converted into kinetic energy at the bottom:
(1)
where
m is the mass of the block
g = 9.8 m/s^2 is the acceleration of gravity
h is the initial height of the block
v is the speed of the block at the bottom
The initial height of the block is equal to the height of the ramp, so
(2)
where
L = 3.00 m is the length of the ramp
is the angle of the ramp
Substituting (2) into (1) and re-arranging the equation, we find the speed
Coefficient of kinetic friction between the floor and the block: 0.3
In the second part of the motion, the block is slowed down by friction along the flat surface. According to the work-energy theorem, the work done by friction is equal to the change in kinetic energy of the block:
where
W is the work done by friction
Kf is the final kinetic energy of the block, which is zero since the block comes to rest
is the initial kinetic energy of the block, where
m = 10.0 kg is the mass of the block
v = 5.42 m/s is its initial speed
Substituting into the equation, we find
and the work is negative, since the direction of the force of friction is opposite to the direction of motion of the block.
Now we can rewrite the work as the product between the force of friction and the displacement of the block:
where
is the coefficient of friction
d = 5.00 m is the displacement of the block
Solving for ,