A child of mass me = 44 kg is in a roller coaster car that travels in a loop of radius R = 7 m. At point A the speed of the car is VA= 10 m/s, and at point B, the speed is vg 10.4 m/s. Assume the child is not holding on and does not wear a seat belt. Assume all quantities are correct to 3 significant figures. B A 30° l.a) Draw a FBD Let NA be the force of the roller coaster car on the child. In your notebook, draw a free body diagram of the child at point A. Draw the vector for the centripetal acceleration at A in the box. A Let NÅ be the force of the roller coaster car on the child. In your notebook, draw a free body diagram of the child at point A. Draw the vector for the centripetal acceleration at A in the box. radial direction p 0 (1.b) Set-up Newton's Second Law along the radial direction at point A in terms of the normal force at A, NA, and the weight of the child, mog, SYMBOLICALLY Note: The radial direction at A (direction along the radius and towards the center is positive) is shown in the figure above. ZF, F+NA-mg=mcac Do not forget the subscripts "c" for the child's mass and the susbcript "A" for the normal when answering the question above.

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A child of mass mc = 44 kg is in a roller coaster car that travels in a loop of radius R = 7 m. At point A
the speed of the car is VA= 10 m/s, and at point B, the speed is VB = 10.4 m/s. Assume the child is
not holding on and does not wear a seat belt.
Assume all quantities are correct to 3 significant figures.
B
R
A
30°
(I.a) Draw a FBD
Let NÅ be the force of the roller coaster car on the child. In your notebook, draw a free body diagram
of the child at point A. Draw the vector for the centripetal acceleration at A in the box.
A
me
radial
direction
ac
(I.a) Draw a FBD
A
Let NÅ be the force of the roller coaster car on the child. In your notebook, draw a free body diagram
of the child at point A. Draw the vector for the centripetal acceleration at A in the box.
A
R
me
TFV 298
radial
direction
ac
0.-)
(1.b) Set-up Newton's Second Law along the radial direction at point A in terms of the normal
force at A, NA, and the weight of the child, mcg, SYMBOLICALLY
Note: The radial direction at A (direction along the radius and towards the center is positive)
is shown in the figure above.
ZF,
F+NA-mg x = mcac
Do not forget the subscripts "c" for the child's mass and the susbcript "A" for the normal when
answering the question above.
done
WOA
Transcribed Image Text:A child of mass mc = 44 kg is in a roller coaster car that travels in a loop of radius R = 7 m. At point A the speed of the car is VA= 10 m/s, and at point B, the speed is VB = 10.4 m/s. Assume the child is not holding on and does not wear a seat belt. Assume all quantities are correct to 3 significant figures. B R A 30° (I.a) Draw a FBD Let NÅ be the force of the roller coaster car on the child. In your notebook, draw a free body diagram of the child at point A. Draw the vector for the centripetal acceleration at A in the box. A me radial direction ac (I.a) Draw a FBD A Let NÅ be the force of the roller coaster car on the child. In your notebook, draw a free body diagram of the child at point A. Draw the vector for the centripetal acceleration at A in the box. A R me TFV 298 radial direction ac 0.-) (1.b) Set-up Newton's Second Law along the radial direction at point A in terms of the normal force at A, NA, and the weight of the child, mcg, SYMBOLICALLY Note: The radial direction at A (direction along the radius and towards the center is positive) is shown in the figure above. ZF, F+NA-mg x = mcac Do not forget the subscripts "c" for the child's mass and the susbcript "A" for the normal when answering the question above. done WOA
(1.c) What is the force of the car seat on the child at point A?
Enter to 3 significant figures
NA = 197
(1.d) What minimum speed is required to keep the child in his seat at point A?
Enter to 3 significant figures
V min = 8.28
N
m
S
(II.a) Draw a FBD
B
In your notebook, draw a free body diagram of the child at point B. Let Ng be the normal force at B.
Draw the vector for the centripetal acceleration at B in the box.
B
me
R
ac
0:
radial direction
(II.b) Set-up Newton's Second Law along the radial direction at point B in terms of the normal
force at B, NB, the weight of the child meg, and 0 SYMBOLICALLY
Note: The radial direction at B (direction along the radius and towards the center is positive)
is shown in the figure above.
= mcac
ΣF,=
Do not forget the subscripts "c" for the child's mass and the susbcript "B" for the normal when
answering the question above.
Transcribed Image Text:(1.c) What is the force of the car seat on the child at point A? Enter to 3 significant figures NA = 197 (1.d) What minimum speed is required to keep the child in his seat at point A? Enter to 3 significant figures V min = 8.28 N m S (II.a) Draw a FBD B In your notebook, draw a free body diagram of the child at point B. Let Ng be the normal force at B. Draw the vector for the centripetal acceleration at B in the box. B me R ac 0: radial direction (II.b) Set-up Newton's Second Law along the radial direction at point B in terms of the normal force at B, NB, the weight of the child meg, and 0 SYMBOLICALLY Note: The radial direction at B (direction along the radius and towards the center is positive) is shown in the figure above. = mcac ΣF,= Do not forget the subscripts "c" for the child's mass and the susbcript "B" for the normal when answering the question above.
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