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A student of weight 659 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force F with arrowN on the student from the seat is 560 N. (a) Does the student feel "light" or "heavy" there? heavy light Correct: Your answer is correct. (b)What is the magnitude of F with arrowN at the lowest point? 758 Correct: Your answer is correct. N (c) If the wheel's speed is doubled, what is the magnitude of F with arrowN at the highest point? N (d) What is the magnitude of F with arrowN at the lowest point under the same conditions as in (c)?

Answer :

santiquirogal

Answer:

a) The student feel light

b) Nbottom = 758 N

c) N'top= 236 N

d) N'bottom= 1055 N

Explanation:

a) W= 659N , Ntop= 560N

W > Ntop ---> Student feel less weight

b)   Top:

∑F= W - Ntop = m.v²/R

m.v²/R = 659N - 560 N = 99 N

Bottom:

∑F= Nbottom- W = m.v²/R

Nbottom= W + m.v²/R = 659N + 99 N = 758N

c) W= 659 N , Ntop= 560 N , v'=2.v

N'top= ?

∑F= W - N'top = m.v'²/R

N'top= W - 4.m.v²/R

N'top = 659 N - 4. 99 N = 263 N

d)   N'bottom = ?

∑Fbottom= N'bottom- W = m.v'²/R

N'bottom = W + 4.m.v²/R = 659 N + 4. 99 N = 1055 N

The normal reaction changes according to Newtons second law of motion

(a) The student feels light

(b) [tex]\overset \rightarrow {F}[/tex] > 659 N

(c) [tex]\overset \rightarrow {F}[/tex] < 560 N

(d) [tex]\overset \rightarrow {F}[/tex] >> 659 N

Reason:

Known parameters;

The weight of the student = 659 N

The magnitude of the normal force at the highest point = 560 N

(a) The normal force reacting to the weight of the student

Given that the normal force at the highest point, is 560 N < 659 N, the weight of the student, the student feels lighter at the highest point

The student feels light

(b) On the way up from the lowest point the acceleration of the student, is given as follows;

Acceleration = a + g

Where;

g = The acceleration due to gravity ≈ 9.81 m/s²

The force acting on the student at the bottom, F = m×(a + g)

The magnitude of F, at the highest point is 758 N

Therefore;

Given that the acceleration experienced by the student is more, the force acting on the student is more

[tex]\overset \rightarrow {F}[/tex] > 659 N

(c) By doubling the speed of the Ferris wheel, at the highest point, the change in momentum is increased, therefore, the normal reaction due to the student weight is lesser and the student feels lighter than 560 N

[tex]\overset \rightarrow {F}[/tex] < 560 N

(d) The magnitude of [tex]\overset \rightarrow {F}[/tex], at the lowest point under the same condition, will result in a change in the momentum that is much larger, such that the normal reaction at the bottom is increased

[tex]\overset \rightarrow {F}[/tex] > 758 N

student

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