Answer:
Explanation:
mass of backpack, m = 8.1 kg
weight of climber, W = 656 N
height raised, h = 9.4 m
time, t = 28.2 min = 28.2 x 60 = 1692 second
weight of backpack, w = m x g = 8.1 x 9.8 = 79.38 N
Work done by the climber on the backpack = mg x h = 79.38 x 9.4 = 746.17 J
Wok done in lifting herself + backpack = (W + w) x h
= (656 + 79.38) x 9.4 = 6912.57 J
Power developed by the climber,P = Total work / time
P = 6912.57 / 1692 = 4.09 W
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
Average acceleration is the ratio of the change in velocity to the time it takes for that change to occur:
We want to find 
:
