Answer:
2.943 J
Explanation:
Data:
acceleration due to gravity, g = 9.81 m/s²
mass of sand = 0.5 kg
distance = 0.6
Thermal energy = the energy possessed by the falling sand
The force of sand = ma
= 
However, the energy is given as the force multiplied by the distance, so
E =fd
Therefore, the thermal energy is 2.943 joules
(a) Differentiate the position vector to get the velocity vector:
<em>r</em><em>(t)</em> = (3.00 m/s) <em>t</em> <em>i</em> - (4.00 m/s²) <em>t</em>² <em>j</em> + (2.00 m) <em>k</em>
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em> = (3.00 m/s) <em>i</em> - (8.00 m/s²) <em>t</em> <em>j</em>
<em></em>
(b) The velocity at <em>t</em> = 2.00 s is
<em>v</em> (2.00 s) = (3.00 m/s) <em>i</em> - (16.0 m/s) <em>j</em>
<em></em>
(c) Compute the electron's position at <em>t</em> = 2.00 s:
<em>r</em> (2.00 s) = (6.00 m) <em>i</em> - (16.0 m) <em>j</em> + (2.00 m) <em>k</em>
The electron's distance from the origin at <em>t</em> = 2.00 is the magnitude of this vector:
||<em>r</em> (2.00 s)|| = √((6.00 m)² + (-16.0 m)² + (2.00 m)²) = 2 √74 m ≈ 17.2 m
(d) In the <em>x</em>-<em>y</em> plane, the velocity vector at <em>t</em> = 2.00 s makes an angle <em>θ</em> with the positive <em>x</em>-axis such that
tan(<em>θ</em>) = (-16.0 m/s) / (3.00 m/s) ==> <em>θ</em> ≈ -79.4º
or an angle of about 360º + <em>θ</em> ≈ 281º in the counter-clockwise direction.
Answer:
x = 0 m
y = 1.02 m
Explanation:
M1 = 2.09 kg
y1 = 2.97 m
M2 = 2.93 kg
y2 = 2.53 m
M3 = 2.57 kg
y3 = 0 m
M4 = 3.92 kg
y5 = -0.496 m
since all objects are situated on the Y-axis, this means the x coordinate of the center of mass is 0.
To find the y coordinate of the center of mass, we apply the equation below.
sum of moment of the objects about the origin = moment of the total mass of objects about the center of mass
M1.y1 + M2.y2 + M3.y3 + M4.y4 = Mt.Y
(2.09 x 2.97) + (2.93 x 2.53) + (2.57 x 0) + (3.92 x -0.496) = (2.09 + 2.93 + 2.57 + 3.92) Y
11.68 = 11.51 Y
Y = 11.68 / 11.51 = 1.02 m
