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: see the graph attached (straight line, passing through the origin and positive slope).
Justification:1)
Kinetic energy and temperature are in direct proportion. That means:
i) Being kinetic energy y and temperature x:
y α xii) That implies:
y = kx,where k is the constant of proportionality.
iii) The graph is a
line that passes through the origin and has positive slope k (k = y / x).2) The proportional relationship between kinetic energy (KE) and temperature (T) is shown by the
Boltzman law, which states:
Average KE = [3 / 2] KT, where K is Boltzman's constant, whose graph is of the form shown in the figure attached.
(-5)/3 - 6/(-5)
You can solve it now :)
Answer:
Explanation:
Kinetic energy generated = work done by force = force x displacement
= 3 x 7 = 21 J