Question

a 60kg skateboarder (including the skateboard) is skating over a hill as shown. when the skateboarder reaches the peak of the hill, he has both feet on the board and is moving 6m/s. neglect any friction and drag impeding the motion as well as the size of the skateboarder. number of forces. force(s) towards center. are all forces balanced? what is the skateboarders centripetal acceleration? what is the centripetal net force on the skateboarder? what is the normal force on the skateboarder?

Explanation:

Step1: Identify given values

Mass $m=60\ \text{kg}$, speed $v=6\ \text{m/s}$, radius $r=9\ \text{m}$, $g=10\ \text{m/s}^2$

Step2: Calculate centripetal acceleration

$\text{Centripetal acceleration } a_c = \frac{v^2}{r} = \frac{6^2}{9} = 4\ \text{m/s}^2$

Step3: Calculate centripetal net force

$\text{Net force } F_c = m \cdot a_c = 60 \times 4 = 240\ \text{N}$

Step4: Calculate normal force

$\text{Weight } W = m \cdot g = 60 \times 10 = 600\ \text{N}$
$\text{Normal force } F_N = W - F_c = 600 - 240 = 360\ \text{N}$

Step5: Analyze force balance

Since there is a net centripetal force, forces are unbalanced. The two forces are weight (downward) and normal force (upward); the net force (toward center) is the difference, so 1 force component acts toward the center.

Answer:

Number of forces: 2
Force(s) towards center: 1
Are all forces balanced? no
What is the skateboarder's centripetal acceleration? $4\ \text{m/s}^2$
What is the centripetal net force on the skateboarder? $240\ \text{N}$
What is the normal force on the skateboarder? $360\ \text{N}$