1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Jlenok [28]
3 years ago
15

A 56.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 22.0 m. (a) What is the

centripetal acceleration of the child? magnitude 1.76 m/s2 direction (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? magnitude 647.4 N direction (c) What force does the seat exert on the child at the highest point of the ride? magnitude 450.2 N direction (d) What force does the seat exert on the child when the child is halfway between the top and bottom? (Assume the Ferris wheel is rotating clockwise and the child is moving upward.) magnitude N direction 79.8 ° counter-clockwise from the horizontal
Physics
1 answer:
Alona [7]3 years ago
3 0

Answer:

a. 3.86 m/s²

b. 332.64 N directed upwards towards the center of the ferris wheel.

c. 764.96 N directed downwards towards the center of the ferris wheel.

d. 589.84 N at 21.5° counterclockwise from the horizontal direction.

Explanation:

a. Since the ferris wheel rotates 4 times per minute, its period, T = 60 s/4 = 15 s.

We now find it angular speed ω = 2π/T = 2π/15 = 0.418 rad/s

We then calculate its centripetal acceleration from a = rω² where r = radius of ferris wheel = 22.0 m.

So, a = 22 m × (0.418 rad/s)² = 3.86 m/s²

b. At the lowest point, the normal force, N and the centripetal force, F both act in opposite directions to the weight, mg of the object. So,

N + F = mg

N = mg - F      

N = mg - ma where a is the centripetal acceleration

N = m(g - a)

N = 56 kg(9.8 m/s² - 3.86 m/s²)

N = 56 kg × 5.94 m/s²

N = 332.64 m/s²

The normal force the seat exerts on the child is thus 332.64 N directed upwards towards the center of the ferris wheel.

c. At the highest point, the weight, mg of the object and the centripetal force, F both act in opposite directions to the normal force, N. So,

N = mg + F      

N = mg + ma where a is the centripetal acceleration

N = m(g + a)

N = 56 kg(9.8 m/s² + 3.86 m/s²)

N = 56 kg × 13.66 m/s²

N = 764.96 N

The normal force the seat exerts on the child is thus 764.96 N directed downwards towards the center of the ferris wheel.

d. Half way between the top and the bottom of the ferris wheel, the normal force must balance the weight and the centripetal force so the child doesn't fall off. For this to happen, the normal force is thus the resultanf of the centripetal force and the weight of the child. Since these two forces are perpendicular at this instance,

N = √[(mg)² + (ma)²] = m√(g² + a²) = 56 kg√[(9.8 m/s²)² + (3.86 m/s²)²] = 56 kg√[(97.196 (m/s²)² + 14.8996(m/s²)²] = 56kg√110.9396 (m/s²)² = 56 kg × 10.53 m/s² = 589.84 N.

Since the centripetal force acts towards the center of the ferris wheel in the horizontal direction, it is equal to the horizontal component of the normal force, Also, the weight acts downwards and is equal to the vertical component of the normal force.

So, the direction of the normal force is gotten from

tanθ = ma/mg = a/g

θ = tan⁻¹(a/g) = tan⁻¹(3.86 m/s² / -9.8 m/s²) = tan⁻¹(-0.3939) = -21.5°. Since the angle is it shows a counter clockwise direction.

So, the normal force is 589.84 N at 21.5° counterclockwise from the horizontal direction.

You might be interested in
How do earthquakes affect boulders
MaRussiya [10]
Weathering and rock slides
5 0
3 years ago
Fear me or i am glory i give you free p oints <br> \ /<br> _| |_
8_murik_8 [283]

Answer:

kayyy

Explanation:

3 0
3 years ago
Read 2 more answers
In an electric field, 0.90 joule of work is required to bring 0.45 coulomb of charge from point a to point
jarptica [38.1K]
The difference in electric potential energy between the two points is
\Delta U = q \Delta V
where q is the magnitude of the charge and \Delta V is the electric potential difference.

But for energy conservation, the difference in electric potential energy \Delta U between the two points is equal to the work done to move the charge between A and B:
W=\Delta U
so we have
W=q \Delta V

and by substituting the numbers of the problem, we find the value of \Delta V:
\Delta V =  \frac{W}{q}= \frac{0.90 J}{0.45 C}=2 V
3 0
2 years ago
What is the difference between a mineral and a rock
Sedbober [7]

A mineral is a naturally occurring, inorganic solid with a definite chemical composition and a crystalline structure formed by geological processes.

A rock is an aggregate of one or more minerals. It may also contain organic remains and mineraloids apart from regular mineral formations. Since rocks vary in their mineral and chemical composition, they are classified according to the process of their formation.

5 0
3 years ago
Read 2 more answers
The needle in the following diagram rotates around a fixed point in the middle. Based on the information given, what way will th
Ronch [10]

Answer:

nods 40th anniversary rid off e 49en9 snns

3 0
3 years ago
Other questions:
  • What is a tool that measures the size of a force
    11·1 answer
  • The school is about 1500 m away. you run toward the school with an average velocity of 3 m per sec. how long did it take you to
    11·2 answers
  • What is the acceleration of a softball if it has a mass of 0.5 kg and hits the cathers glove with a force of 25n
    5·1 answer
  • What is the function of the Cytoplasm?
    7·1 answer
  • What is the main structure of lymphatic system?
    10·2 answers
  • The smallest possible part of an element that can still be identified as the element is called
    11·1 answer
  • A runner starts slowing down as she gets tired. At 10 seconds, she 8m/a, and slows down to 2m/a at 13 seconds. What is her accel
    13·1 answer
  • Se tiene un objeto a una altura de 8 m generando 450 J de energía potencial cuál es la masa de dicho objeto
    12·1 answer
  • For a system mass of 600g and a hanging weight of 0.50 N, determine the acceleration of the system
    13·1 answer
  • 1. A silicon BJT is connected as shown in Fig 1, where RC = 3.6 k 2. VBE = 0.8 V. (10%)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!