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
Answer:
(A) The speed just as it left the ground is 30.25 m/s
(B) The maximum height of the rock is 46.69 m
Explanation:
Given;
weight of rock, w = mg = 20 N
speed of the rock at 14.8 m, u = 25 m/s
(a) Apply work energy theorem to find its speed just as it left the ground
work = Δ kinetic energy
F x d = ¹/₂mv² - ¹/₂mu²
mg x d = ¹/₂m(v² - u²)
g x d = ¹/₂(v² - u²)
gd = ¹/₂(v² - u²)
2gd = v² - u²
v² = 2gd + u²
v² = 2(9.8)(14.8) + (25)²
v² = 915.05
v = √915.05
v = 30.25 m/s
B) Use the work-energy theorem to find its maximum height
the initial velocity of the rock = 30.25 m/s
at maximum height, the final velocity = 0
- mg x H = ¹/₂mv² - ¹/₂mu²
- mg x H = ¹/₂m(0) - ¹/₂mu²
- mg x H = - ¹/₂mu²
2g x H = u²
H = u² / 2g
H = (30.25)² / 2(9.8)
H = 46.69 m
Voltage (V)= Current (I) * Resistance (R)
I=V/R=140/2=70A
Hope this helps!
