A lion chasing a zebra sprints 200 meters in ten seconds what is the lions average speed

How many revolutions per minute would a 23 m -diameter Ferris wheel need to make for the passengers to feel "weightless" at the

kirza4 [7]

Answer:

Approximately $6.2\; {\rm rpm}$ , assuming that the gravitational field strength is $g = 9.81\; {\rm m\cdot s^{-2}}$ .

Explanation:

Let $\omega$ denote the required angular velocity of this Ferris wheel. Let $m$ denote the mass of a particular passenger on this Ferris wheel.

At the topmost point of the Ferris wheel, there would be at most two forces acting on this passenger:

Weight of the passenger (downwards), $m\, g$ , and possibly
Normal force $F_\text{normal}$ that the Ferris wheel exerts on this passenger (upwards.)

This passenger would feel "weightless" if the normal force on them is $0$ - that is, $F_\text{normal} = 0$ .

The net force on this passenger is $(m\, g - F_\text{normal})$ . Hence, when $F_\text{normal} = 0$ , the net force on this passenger would be equal to $m\, g$ .

Passengers on this Ferris wheel are in a centripetal motion of angular velocity $\omega$ around a circle of radius $r$ . Thus, the centripetal acceleration of these passengers would be $a = \omega^{2}\, r$ . The net force on a passenger of mass $m$ would be $m\, a = m\, \omega^{2}\, r$ .

Notice that $m\, \omega^{2} \, r = (\text{Net Force}) = m\, g$ . Solve this equation for $\omega$ , the angular speed of this Ferris wheel. Since $g = 9.81\; {\rm m\cdot s^{-2}}$ and $r = 23\; {\rm m}$ :

$\begin{aligned} \omega^{2} = \frac{g}{r}\end{aligned}$ .

$\begin{aligned} \omega &= \sqrt{\frac{g}{r}} \\ &= \sqrt{\frac{9.81\; {\rm m \cdot s^{-2}}}{23\; {\rm m}}} \\ &\approx 0.653\; {\rm rad \cdot s^{-1}} \end{aligned}$ .

The question is asking for the angular velocity of this Ferris wheel in the unit ${\rm rpm}$ , where $1\; {\rm rpm} = (2\, \pi\; {\rm rad}) / (60\; {\rm s})$ . Apply unit conversion:

$\begin{aligned} \omega &\approx 0.653\; {\rm rad \cdot s^{-1}} \\ &= 0.653\; {\rm rad \cdot s^{-1}} \times \frac{1\; {\rm rpm}}{(2\, \pi\; {\rm rad}) / (60\; {\rm s})} \\ &= 0.653\; {\rm rad \cdot s^{-1} \times \frac{60\; {\rm s}}{2\, \pi\; {\rm rad}} \times 1\; {\rm rpm} \\ &\approx 6.2\; {\rm rpm} \end{aligned}$ .

3 0

1 year ago

The primary purpose in creating national parks is to _____. protect the land from development and pollution provide locations fo

zzz [600]

Answer:

The primary purpose in creating national parks is to protect the land from development and pollution.

Explanation:

National parks are owned by the national government. This areas are strictly reserved for habitat of wild animals.

The main purpose for creating national parks is to reserve some space for nature. This area is protected from pollution and development.

Thus, answer for given question is protect the land from development and pollution.

4 0

3 years ago

The tires of a car support the weight of a stationary car. If one tire has a slow leak, the air pressure within the tire will __

Kipish [7]

Answer:

The tires of a car support the weight of a stationary car. If one tire has a slow leak, the air pressure within the tire will decrease with time, the surface area between the tire and the road will increase with time, and the net force the tire exerts on the road will be constant with time.

Explanation:

when a wheel has an air leak, it means that the inside of the tire has less air, which means that there will be less air pushing the walls of the tire so that the air pressure decreases.

On the other hand, the tire begins to deform due to lack of air which increases the area of contact with the floor.

As the weight of the car remains constant and the air has a negligible mass the force towards the road will be the same

4 0

3 years ago

The tension in the rope securing the upper pulley and the force that must be applied to keep the system in equilibrium

chubhunter [2.5K]

Answer:

Explanation:

In a frictionless system with no acceleration, the tension in the rope must be F along its entire length

FBD analysis of the lower pulley has two upward acting tension vectors F and one downward acting weight vector W

2F = W

F = W/2

FBD analysis of the upper pulley has one upward acting support vector T and three downward acting tension vectors F

T = 3F

T = 3(W/2)

T = 1.5W

8 0

2 years ago

Many people love roller coasters. Some people call them scream machines. They agree that

Alex73 [517]

Answer:

There is some sort of "rollers" on the trail part that is used to make the roller coaster move when it is going up. Then because of that, the speed gets quicker when it drops down, so then it could move for a longer time until it reaches the next arch.

Explanation:

hope this helps :)

4 0

2 years ago