# Vertical Circular Motion problem

## Homework Statement

A motorcycle has a constant speed of 25.0m/s as it passes over the top of a hill whose radius of curvature is 126m. The mass of the motorcycle and driver is 342kg. Find the magnitudes of (a) the centripetal force and (b) the normal force the acts on the cycle

Fc = (mv^2)/r
W = mg

## The Attempt at a Solution

Well for part a I got the right answer,
Fc = (mv^2)/r
Fc = 342(25^2)/r
Fc = 1696N => 1.70 x 10^3N

however for part b i got the wrong answer. this is my thinking
Since centripetal force always points towards the centre, and since the motorcycle is at the top of the hill, then the net force in the y direction is equal to = N-Fc-W
Therefore N = Fc + W
N = 1696 + mg
N = 1696 + (342)(9.8)
N = 5047.6
however the right answer is 1.66 x 10^3N

PhanthomJay
Homework Helper
Gold Member

## Homework Statement

A motorcycle has a constant speed of 25.0m/s as it passes over the top of a hill whose radius of curvature is 126m. The mass of the motorcycle and driver is 342kg. Find the magnitudes of (a) the centripetal force and (b) the normal force the acts on the cycle

Fc = (mv^2)/r
W = mg

## The Attempt at a Solution

Well for part a I got the right answer,
Fc = (mv^2)/r
Fc = 342(25^2)/r
Fc = 1696N => 1.70 x 10^3N

however for part b i got the wrong answer. this is my thinking
Since centripetal force always points towards the centre, and since the motorcycle is at the top of the hill, then the net force in the y direction is equal to = N-Fc-W
Therefore N = Fc + W
N = 1696 + mg
N = 1696 + (342)(9.8)
N = 5047.6
however the right answer is 1.66 x 10^3N

I am not sure whether you are incorrectly trying to use newton's first law when it should be his second, or else just misunderstanding the centripetal force concept. You correctly calculated the centripetal force, which is the net inward force comprised of the weight and normal forces. The centripetal force is not a force of its own. It is a net force which is the vector sum of the normal and weight forces in the inward direction.

I am not sure whether you are incorrectly trying to use newton's first law when it should be his second, or else just misunderstanding the centripetal force concept. You correctly calculated the centripetal force, which is the net inward force comprised of the weight and normal forces. The centripetal force is not a force of its own. It is a net force which is the vector sum of the normal and weight forces in the inward direction.

Why is centripetal force not a force on its own? If centripetal force is the net inward force comprised of the weight and normal forces then,
Fc = N-W
N = Fc+W
and i still get the same thing? since the motorcycle is on top of the hill then normal force is upward and weight is downward hence the "N-W"

PhanthomJay
Homework Helper
Gold Member
Why is centripetal force not a force on its own? If centripetal force is the net inward force comprised of the weight and normal forces then,
Fc = N-W
N = Fc+W
and i still get the same thing? since the motorcycle is on top of the hill then normal force is upward and weight is downward hence the "N-W"
Net force always acts in the direction of the acceleration. The acceleration, centripetal in this example, is inward, or down. Thus the net force must be inward, or down. If the net force is down, the weight must be greater than the normal force, right?

Net force always acts in the direction of the acceleration. The acceleration, centripetal in this example, is inward, or down. Thus the net force must be inward, or down. If the net force is down, the weight must be greater than the normal force, right?

ok so if net force acts in the direction of acceleration, and centripetal acceleration is downward.
then fc is negative. so, -Fc = N-W
N = Fc-W

?? is this correct

PhanthomJay
Homework Helper
Gold Member
You are continuing to treat Fc as a force of its own. It is not. Try Newton 2:

$F_{net} = ma$
$F_{net} = mv^2/r$
$mg - N = mv^2/r$
$mg - N = F_c$

Solve for N.

Note that the centripetal force is the net inward force that is the vector sum total, or net if you will, or resultant , of all forces acting in the inward direction. In uniform circular motion, the acceleration is inward, and the net force is thus inward, toward the center of the circle. Because the net force acts toward the center of the circle, it is called a centripetal, or center seeking, force.

You are continuing to treat Fc as a force of its own. It is not. Try Newton 2:

$F_{net} = ma$
$F_{net} = mv^2/r$
$mg - N = mv^2/r$
$mg - N = F_c$

Solve for N.

Note that the centripetal force is the net inward force that is the vector sum total, or net if you will, or resultant , of all forces acting in the inward direction. In uniform circular motion, the acceleration is inward, and the net force is thus inward, toward the center of the circle. Because the net force acts toward the center of the circle, it is called a centripetal, or center seeking, force.

In the equation Fc = mg - N
why is n treated as a negative

PhanthomJay
Homework Helper
Gold Member
It is an arbitrary use of signage. N is treated as negative, up, and mg is treated as positive, down. Acceleration, which acts down, is then also treated as a plus.

You can reverse signs, using up plus and minus down, and get the same result. Looks like you tried that
ok so if net force acts in the direction of acceleration, and centripetal acceleration is downward.
then fc is negative. so, -Fc = N-W
N = Fc-W
but your algebra was not so good, should be N = W -Fc.

I find it easier to choose the direction of the acceleration as plus, but it is a personal choice that helps with minus sign errors. The choice however is yours.

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