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:
Option C
Maximum potential energy is at point R.
Explanation:
Potential energy is a product of mass, acceleration due to gravity and height ie
PE=mgh where PE is the potential energy, m is mass of an object, g is acceleration due to gravity whose value is normally taken as 9.81 and h is height. Since at point R we have the maximum height, the potential energy will be highest at this point.
Explanation:
It is given that,
Velocity of the particle moving in straight line is :
We need to find the distance (x) traveled by the particle during the first t seconds. It is given by :
Using by parts integration, we get the value of x as :
Hence, this is the required solution.
Answer:
995 N
Explanation:
Weight of surface, w= 4000N
Gravitational constant, g, is taken as 9.81 hence mass, m of surface is W/g where W is weight of surface
m= 4000/9.81= 407.7472
Using radius of orbit of 6371km
The force of gravity of satellite in its orbit, 
Where 
and 
F= 995.01142 then rounded off
F=995N
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