Hi Lilyana R.!
Solving this problem involves using centripetal acceleration as part of our Newton's 2nd Law equation.
However, we must always consider the position of the cart with these vertical circular motion problems. Additionally, we must be careful to consider whether the cart is positioned at the top of a hill or loop. For example, when the cart is positioned at the top of a loop, both the force due to gravity (weight) and the normal force point in the same direction, inwards toward the center. On the other hand, when the cart is at the top of a hill, the normal force points in the upward direction--away from the center of the circle--and the force due to gravity points downward into the center of the circle.
Additionally, in any circular motion question, we take the center of the circle to be the positive direction.
Let's have a look over our Newton's 2nd Law equation:
∑Fy = Fg - n = mac
As we discussed above, we have taken the forces pointing inwards toward the center of the circle as positive--in this case, the force due to gravity--and those pointing away from the center of the circle as negative--the normal force. We have set this equal to the mass multiplied by the acceleration. However, our acceleration is the centripetal acceleration, ac. Centripetal acceleration is defined as:
ac = v2/r
In which case, we want to substitute that into our equation, and then rearrange to solve for the normal force:
Fg - n = mac = m(v2/r) => n = Fg - m(v2/r) = m(g - v2/r)
We may now plug in our values and solve:
<=> (800kg)[9.8 m*s-2 - [(4 m*s)2)/7m]
n = 6 x 103 N
Hope his helps!
Cheers
