Answer:
[ 2.67 , 1 ] m
Explanation:
Given:-
- The side lengths of the rods are as follows:
a = 4 m , b = 4 m , c = 5 m
a = Base , b = Perpendicular , c = Hypotenuse
- All rods are made of same material with uniform density. With
Find:-
Find the coordinates of the center of mass of the triangle.
Solution:-
- The center of mass of any triangle is at the intersection of its medians.
- So let’s say we have a triangle with vertices at points (0,0) , (a,0) , and (0,b).
- Median from (0,0) to midpoint (a/2,b/2) of opposite side has equation:
bx−ay=0
- Median from (a,0) to midpoint (0,b/2) of opposite side has equation:
bx+2ay=ab
- Median from (0,b) to midpoint (a/2,0) of opposite side has equation:
2bx+ay=ab
- Solve all three equations simultaneously:
bx−ay=0 , bx = ay
ay + 2ay = ab , 3ay = ab , y = b/3
bx = b/3
x = a / 3
- So the distance from the median to each leg of the triangle is 1/3 length of other leg.
- So the coordinates of the centroid for right angle triangle would be:
[ 2a/3 , b/3 ]
[ 2.67 , 1 ] m
Answer:
a) K = 2/3 π G m ρ R₁³ / R₂
, b) U = - G m M / r
Explanation:
The law of universal gravitation is
F = G m M / r²
Part A
Let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / R₂
G m M / R₂² = m v² / R₂
v² = G M / R₂
They give us the density of the planet
ρ = M / V
V = 4/3 π R₁³
M = ρ V
M = ρ 4/3 π R₁³
v² = 4/3 π G ρ R₁³ / R₂
K = ½ m v²
K = ½ m (4/3 π G ρ R₁³ / R₂)
K = 2/3 π G m ρ R₁³ / R₂
Part B
Potential energy and strength are related
F = - dU / dr
∫ dU = - ∫ F. dr
The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1
U- U₀ = G m M ∫ dr / r²
U - U₀ = G m M (- r⁻¹)
We evaluate for
U - U₀ = -G m M (1 / 
- 1 /
)
They indicate that for ri = ∞ U₀ = 0
U = - G m M / r
Answer:
Impulse = 80Ns
Explanation:
Given the following data;
Mass = 3kg
Force = 20N
Time = 4 seconds
To find the impulse experienced by the object;
Impulse = force * time
Impulse = 20*4
Impulse = 80Ns
Therefore, the impulse experienced by the object is 80 Newton-seconds.
Answer:
the angular velocity of the car is 12.568 rad/s.
Explanation:
Given;
radius of the circular track, r = 0.3 m
number of revolutions per second made by the car, ω = 2 rev/s
The angular velocity of the car in radian per second is calculated as;
From the given data, we convert the angular velocity in revolution per second to radian per second.
Therefore, the angular velocity of the car is 12.568 rad/s.
The work done by the applied force on the block against the frictional force is 15.75 J.
<h3>
Work done by the applied force</h3>
The work done by the applied force is calculated as follows;
W = Fd
F - Ff = ma
where;
- F is applied force
- Ff is frictional force
Fcos(37) - μmgsin(37) = ma
Fcos(37) - (0.3)(4)(9.8)sin(37) = 4(0.2)
0.799F - 7.077 = 0.8
F = 9.86 N
W = Fdcosθ
W = 9.86 x 2 x cos(37)
W = 15.75 J
Thus, the work done by the applied force on the block against the frictional force is 15.75 J.
Learn more about work done here: brainly.com/question/25573309
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