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
For this car, predict the shape of a graph that shows distance (x) versus time (t). Note that time is the independent variable a
Mrrafil [7]
Hope this helps!

ANSWER:

5 0
3 years ago
Where does energy come from that fuels our physical activity
joja [24]

Energy comes from the Sun, plants and animals that we eat, to provide us with nutrients we need for energy.


7 0
3 years ago
Read 2 more answers
Can someone help me?
Setler [38]

Answer: (1, 30), (2,10), (3,40), (4,20)

Explanation:

4 0
3 years ago
A __________ painted curb designates an area where there is no stopping, parking, loading, or standing.
Vedmedyk [2.9K]
The answer to this question is the red painted curb. The red painted curb means that the vehicle is not suppose to stop and park in the red curb. It also means that people should not stand in that area. Red painted curb also marks as a fire lane for schools.
4 0
3 years ago
A small mirror is attached to a vertical wall, and it hangs a distance of 1.87 m above the floor. The mirror is facing due east,
Oksana_A [137]

Answer:

 t = 1.62 h

Explanation:

A flat mirror fulfills the law of reflection where the incident angle is equal to the reflected angle.

          θ_i = θ_r

If we use trigonometry to find the angles, the mirror is at a height of L = 1.87 m,   and the reflected rays reach a distance x1 = 3.56 m

         tan θ₁ = x₁ / L

         tan θ₁ = \frac{3.56}{1.87}

         θ₁ = tan⁻¹  1.90

         θ₁ = 62.29º

for the second case x₂ = 1.46 m

        tan θ₂ = x₂ / L

        θ₂ = tan⁻¹  \frac{1.46}{1.87}

        θ₂ = 37.98º

the difference in degree traveled is

         Δθ = θ₁- θ₂

          Δθ = 62.29 - 37.98

          Δθ = 24.31º

as in the exercise they indicate that every 15º there is an hour

         t = 24.31º (1h / 15º)

         t = 1.62 h

4 0
3 years ago
Other questions:
  • The American Psychological Association is the only organization that can approve psychological research studies.
    8·1 answer
  • If you push a cork into the neck of a bottle filled with air, what happens to the pressure inside the bottle?
    12·1 answer
  • According to the first law of thermodynamics, what could happen when heat is added to a system?
    13·2 answers
  • Suppose a certain car supplies a constant deceleration of A meter per second per second. If it is traveling at 90km/hr. When. th
    8·1 answer
  • The conductors that carry the current to electrical devices and ? equipment are the heart of all electrical systems. There are a
    5·1 answer
  • I need help on this science
    8·1 answer
  • (25 Brainly Points.)
    14·1 answer
  • A 6.0 kg mass is placed on a 20º incline which has a coefficient of friction of 0.15. What is the acceleration of the mass down
    15·1 answer
  • place the compass at one pole of the bar magnet click flip polarity in the menu what happens to the bar magnet and the compass n
    6·1 answer
  • How much force to move 18 kg at a rate of 3m/s​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!