Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
Answer:
Explanation:
Using the principle of moment, assuming the rod is uniform rod of mass 1 kg
the center of mass of the rod will be at 1 m
assuming the system is in equilibrium,
clockwise moment = anticlockwise moment
let the distance of the man shoulder be x from the center of gravity and also is the pivot point
total mass of bucket + mass of honey = 2kg + 3 kg = 5 kg for rear bucket and
2kg + 5 kg = 7 kg for front bucket
( 5kg × ( 1+x)) + ( 1 kg × x) = 7 kg × ( 1 - x)
5 + 5 x + x = 7 - 7x
5 + 6x = 7 - 7x
6x + 7x = 7 - 5
13x = 2
x = 2 / 13 = 0.154 m
the honeybucket man's shoulder is 0.154 m from the center of the pole ( forward ).
Answer:
The following is an example of how humans can increase biodiversity
Provide Wildlife Corridors and Connections Between Green Spaces
Use Organic Maintenance Methods and Cut Back On Lawns
Use a Native Plant Palette and Plant Appropriately
Utilize Existing Green Space Connections
Be Mindful of Non-Native Predators
Answer:
Two times as much
Explanation:
The equation for gravitational force is: Fg = GMm/r^2 with G being the universal gravitational constant.
So to make things easier we'll set r equal to 1 since it's a constant as well as G.
Then we're left with Fg=Mm with M being the mass of the sun and m being the mass of the earth.
So if m is constant and supposedly equals 1 then Fg=M so Fg is proportional to M therefore if M doubles then Fg doubles.
