What is the average velocity of the particle from rest to 15 seconds?

A.) 1.1 meters/second
B.) 1.2 meters/second
C.) 1.3 meters/second
D.) 1.4 meters/second

The ratio of the Normal force to the gravitational force of the roller coaster at the top of the circle is [tex]\boxed3[/tex].

Further Explanation:

The critical velocity of the roller coaster is the minimum speed at which the roller coaster completes the circular loop without leaving the path.

As the roller coaster reaches at the topmost point of its circular path, at this point, the weight is balanced by the centripetal force acting in the outward direction.

The force balancing at the top most point at the critical velocity is:

[tex]{\text{Centripetal}}\,{\text{force}} = {\text{weight}}[/tex]

[tex]\dfrac{{mv_c^2}}{r} = mg[/tex]

From the above equation, the critical velocity of the roller coaster is:

[tex]{v_c} = \sqrt {rg}[/tex]

Now, if the roller coaster reaches the top point of the circular path with the speed twice of the critical speed, then there will be a normal reaction force experienced by the roller coaster due to the increased centripetal force.

The new velocity of the roller coaster is:

[tex]\begin{aligned}v&=2{v_c}\\&= 2\sqrt {rg}\\\end{aligned}[/tex]

The force balancing at the top most point at the critical velocity is:

[tex]\begin{aligned}{F_C} = {F_N} + {F_{wt}}\hfill\\\frac{{m{v^2}}}{r} = {F_N} + mg\hfill\\\end{aligned}[/tex]

Here, [tex]{F_C}[/tex] is the centripetal force, [tex]{F_N}[/tex] is the normal reaction acting on the roller coaster and [tex]{F_{wt}}[/tex] is the weight of the roller coaster acting in downward direction.

Substitute [tex]2\sqrt {rg}[/tex] for [tex]v[/tex] in above equation.

[tex]\begin{aligned}\frac{{m{{\left( {2\sqrt {rg} }\right)}^2}}}{r} &= {F_N} + mg\\{F_N} &= 4mg - mg\\&= 3mg\\\end{aligned}[/tex]

The ratio of the normal reaction of the roller coaster to the weight of the roller coaster is:

[tex]\begin{aligned}\frac{{{F_N}}}{{{F_{wt}}}}&=\frac{{3mg}}{{mg}}\\&=3\\\end{aligned}[/tex]

The ratio of the Normal force to the gravitational force of the roller coaster at the top of the circle is  [tex]\boxed3[/tex].

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Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Circular motion

Keywords:  Roller coaster, loop, critical speed, normal reaction, ratio, centripetal force, gravitational force, twice the critical speed, circular loop.

Answer:

To help Jaywon and all others out there, the answer is D

Explanation:

Jaywon and I both took the test and that is the answer.

Explanation:

It is given that,

Mass of the bowling ball, m = 7 kg

We need to find the weight in pounds of 7 kg bowling ball in pounds. Firstly, we need to find the relationship between kilogram and pound. It is as follows :

1 kilograms = 2.204 pounds

The given mass of 7 kilograms can be converted to pounds by using the unitary method as :

[tex]7\ kilograms=(7\times 2.204)\ pounds[/tex]

7 kg = 15.428 pounds

Hence, the weight of bowling ball is 15.428 pounds. Hence, this is the required solution.

Final answer:

OPTION D.

The best representation of scientific laws is that they are factual descriptions of observed phenomena in nature, often expressed through mathematical equations and supported by extensive scientific evidence.

Explanation:

The statement that best represents scientific laws is D. Scientific laws are descriptions of observed phenomena generally accepted as facts. Unlike scientific theories, which provide explanations for phenomena, scientific laws describe the patterns we observe in nature and are often expressed concisely, typically through mathematical equations. A scientific law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and observed through repeated experiments. An example would be Newton's second law of motion, represented by the equation F = ma, which describes the relationship between force (F), mass (m), and acceleration (a).

The archer's problem is a projectile motion question in physics, where the release angle and trajectory concerning an obstruction must be calculated using the range and maximum height formulas, considering the given initial conditions of speed and distance.

The question involves calculating the angle of release for an arrow to hit a target located at a certain distance, as well as considering the arrow's trajectory relative to an obstruction. This is a common projectile motion problem in physics.

Part (a): Finding the Release Angle

To solve for the angle, we can use the equation for the range of a projectile: R =  (v²×sin²(θ))  / g, where R is the range (75.0 m), v is the initial velocity (35.0 m/s), g is the acceleration due to gravity (9.80 m/s^2), and θ is the angle of release. We rearrange the equation to solve for θ and find that there are two possible angles that satisfy the equation because of the sin(2θ) term.

Part (b): Checking if the Arrow Clears the Branch

To determine if the arrow goes over or under the branch, we need to calculate the maximum height (H) of its trajectory. Using the formula H = (v²×sin²(θ)) / (2g), we find that the maximum height of the trajectory depends on the angle of release. With proper substitution and solving, we can determine whether the arrow will clear the 3.50 m high branch.

Final answer:

Using the kinematic equation for velocity, v = u + at, with an initial velocity of 0, an acceleration of 3 m/s^2, and a time of 10 seconds, the motorcycle's velocity will be 30 m/s. So the correct option is B.

Explanation:

If a motorcycle starts from rest and maintains a constant acceleration of 3 m/s2, we can calculate its velocity after a certain time using the kinematic equation v = u + at, where:

Now, substituting the known values into the equation:

v = 0 + (3 m/s2 × 10 s) = 30 m/s

Therefore, the motorcycle's velocity after 10 seconds will be 30 m/s, which corresponds to answer choice B.

The answer is true, midude! Calm down.

Answer: The given statement is true.

Explanation:

In operant conditioning, the events or circumstances to which an individual reacts helps in a certain kind of learning because of their outcome or consequences.

And on the basis of an individual's behavior he gets rewards or punishment.

For example, a child was made to finish his homework first and only then he can go to play. So, the child finishes his homework quickly and as a result of this his mother rewarded him with a chocolate.

Therefore, we can conclude that the statement, in operant conditioning, the consequence shapes the behavior, is true.

Answer:

Einstein

Explanation:

Many physicists and mathematicians, notably Albert Einstein, tried to unify the electromagnetic and gravitational force, that is, made a unified field theory.

Other scientists who attempted to develop unified field theory included Hermann Weyl, Arthur Eddington, and Theodor Kaluza. Unfortunately, all attempts were unsuccessful

Non-renewable sources of energy include fossil fuels like coal, petroleum, and natural gas, as well as nuclear energy. They are called non-renewable because they cannot be replenished within a human timescale and have limited reserves.

A nonrenewable source of energy is one that is finite and cannot be replenished within a human timescale. The most important non-renewable energy sources are fossil fuels, which include coal, petroleum, and natural gas. These resources account for about 81% of the world's energy consumption. Fossil fuels take millions of years to form and are thus considered nonrenewable. Burning these fuels releases energy that can be converted to generate electricity. Another key non-renewable energy source is nuclear energy, which, while supplying about 3% of the world's consumption, also cannot be quickly replenished and has environmental and health costs associated with it, such as the safety and disposal of nuclear waste.

Answer:

8.45m/s^2

Explanation:

a = m2g / m1+m2

63 + 10 = 73 kg

63*9.8 / 73 = 8.45m/s^2

The magnitude of the acceleration of the block when the other block is released would be 8.466 m/s²

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

The mathematical expression for Newton's second law is as follows

F = ma

As given in the problem A 10.0 kg block on a table is connected by a string to a 63 kg mass, which is hanging over the edge of the table. assuming that frictional forces may be neglected,

The force responsible for the motion is only due to the hanging mass of 63Kg  because of the gravitational pull of the earth

F = mg  

  = 63×9.81 N

  =618 N

the acceleration would be the same for both the block as both are connected by a string

a = F/(m₁+m₂)

a = 618/(63+10)

a = 8.466 m/s²

Thus , The magnitude of the acceleration of the block when the other block is released would be 8.466 m/s²

Learn more about Newton's second law, here

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Answer:

The radius of the roller coaster loop is 6.3 m.

Explanation:

It is given that,  

Time taken by roller coaster, t = 3.1 s

Centripetal acceleration, [tex]a_c=26\ m/s^2[/tex]

Velocity in a circular path is given by :

[tex]v=\dfrac{2\pi r}{t}[/tex]  

Centripetal acceleration, [tex]a_c=\dfrac{v^2}{r}[/tex]

So, acceleration, [tex]a_c=\dfrac{4\pi^2r}{t^2}[/tex]

[tex]r=\dfrac{a_ct^2}{4\pi^2}[/tex]

[tex]r=\dfrac{26\times 3.1^2}{4\pi^2}[/tex]

r =6.3 m

So, the correct option is (A) " r = 6.3 m". Hence, this is the required solution

Answer:

r = 6.32 meters

Explanation:

Given that,

The centripetal acceleration acting on the roller coaster, [tex]a_c=26\ m/s^2[/tex]

Time taken by the car, t = 3.1 s

The centripetal acceleration act on an object when it moves in circular path. Its formula is given by :

[tex]a_c=\dfrac{v^2}{r}[/tex]

v is the velocity of car, [tex]v=\dfrac{2\pi r}{t}[/tex]

[tex]a_c=\dfrac{(\dfrac{2\pi r}{t})^2}{r}[/tex]

On rearranging above equation,

[tex]r=\dfrac{a_ct^2}{4\pi ^2}[/tex]

[tex]r=\dfrac{a_ct^2}{4\pi ^2}[/tex]

[tex]r=\dfrac{26\times (3.1)^2}{4\pi ^2}[/tex]

r = 6.32 meters

So, the radius of the roller coaster loop is 6.3 meters. Hence, this is the required solution.

Answer

You should still ensure you are steering straight in the direction of skidding.

Take your foot off the brake unless you are about to hit something. steer in the direction of the skid to straighten your car.

Answer:

Steer your car sideways to the direction of the skid.

Explanation:

Skids happen because the tires of your car don´t have enough traction with the floor, this creates for a slippery situation where the car has no controllable direction, you should not break, but instead try and move the tires in the direction of the skid and then re-gain control of the car.

Answer:

Gravitational acceleration at planet x will be [tex]g=3m/sec^2[/tex]

Acceleration due to gravity on planet x will be less than acceleration due to gravity on earth

Explanation:

We have given mass of the hammer m = 3 kg

And weight of the hammer at planet x = 9 N

We know that weight of the body is given by [tex]W=mg[/tex]

[tex]9=3\times g[/tex]

[tex]g=3m/sec^2[/tex]

So gravitational acceleration at planet x will be [tex]g=3m/sec^2[/tex]

As we know that acceleration due to gravity on earth is [tex]9.8m/sec^2[/tex]

So acceleration due to gravity on planet x will be less than acceleration due to gravity on earth

Answer:

Your answer would be b 120 n toward the front of the boat

Explanation:

I took this test and got this correct, here's proof

Hope you get a good grade, from a fellow comrade

Answer:

Explained

Explanation:

According to the humanistic perspective  securing the future motivates the individuals the most.

All we humans do in our life is somehow trying to secure a future for our selves and our children.

let me explain to you how this happens, basically all our lives we try to get the best education and work hard. Why is that so? It is because we get knowledge and can get some good profession?

But what does a good profession guarantees us? That is monetary and other such benefits, but what do we have to do with all of the money. That is to secure our future. So basically we want to make our future better.