Where are the metals located on the periodic table

Answers

Answer 1

The periodic table on the left separates elements into three groups: the metals (green in the table), nonmetals (orange), and metalloids (blue). Most elements are metals. They are usually shiny, very dense, and only melt at high temperatures.

Answer 2
Final answer:

On the periodic table, representative metals are on the left side, transition metals and inner transition metals are in the centre. Transition metals are found in groups 3-11, while inner transition metals are in the bottom two rows. The reactivity of these metals varies, affecting how they are isolated from ores.

Explanation:

In the periodic table, the metals are generally located on the left side and in the centre. Specifically, representative metals are located on the left side of the table, while transition metals and inner transition metals can be found in the middle. The elements boron, silicon, germanium, arsenic, antimony, and tellurium, known as metalloids or semimetals, act as a divider between metals and nonmetals.

Transition metals are further differentiated as they are located in groups 3-11 of the periodic table and are characterized by their partially filled d orbitals. The inner transition metals are located in the two rows at the bottom of the periodic table, below group 3.

The reactivity of these metal groups varies, from the highly active metals such as scandium and iron, to almost inert elements, like platinum. This variety in reactivity determines the methods used to isolate the elements from their ores, with more active metals being more difficult to reduce.

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Related Questions

Which is a chemical property that can be used to identify calcium carbonate?
A. white color
B. powered solid
C. melting point of 825 °C (1517 °F)
D. reacts with acids by producing gas bubbles

Answers

(D) reacts with acids by producing gas bubbles
Or
(A) White Color

Answer:

could someone at least give one answer instead of a choice between two cause that is a 50/50 chance to get it correct on a test!!

Explanation:

All objects in motion have what energy

Answers

Hello  Undeadman12

All objects in motion would have kinetic energy

:)

Hi there.

Your Question: All objects in motion have what energy ?

Kinetic Energy is the answer,  (I took this part from google) Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).

I hope this helps, if it does, please consider marking me brainiest! <3


I'm in dire need of some help, The first correct response receives brainlest!

A 1,000 g ball and a 100 g ball are both dropped from a tower. both balls have the same size and there is no air resitance. Which one hits the ground first?
A. The 100 g mass hits the ground first
B. The 1000 g mass hits the ground first
C. They both hit at the same time

Answers

C. They both hit at the same time

If they're dropped from the same height at the same time and there's no air resistance, the the lighter ball and the heavier ball, as well as a feather, a hammer, a bowling ball, a speck of dust, a school bus, and a battle ship, will all fall side-by-side and hit the ground at the same time.  

We've known this for about 400 years, since Galileo.  And we've known WHY for about 300 years, since Newton.

Is thallium a solid liquid or gas

Answers

Thallium is a solid.

It its normal state its considered a solid. Its melting points is 304 decrease C.
Atomic weight: 204.383

Hope this helps

Thallium (Tl) is a solid at room temperature. It has a melting point of 304 degrees Celsius and a boiling point of 1,473 degrees Celsius.

Thallium (Tl) is a chemical element that is classified as a metal. At standard temperature and pressure conditions, thallium exists in a solid state. This means that it maintains a fixed shape and volume.

The state of matter of an element or compound is determined by its melting and boiling points.

However, at room temperature (around 25 degrees Celsius), thallium remains in its solid state. It has a metallic appearance and is relatively soft and malleable.

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how much work is done when you push a crate horizontally with 130 N across a 5.0-m

Answers

Complete solution is given below in attachment

What happens to the temperature of the water inside the beaker after all of the ice melts? Why?

Answers

Final answer:

After all the ice has melted, the temperature of the water inside the beaker starts to increase. The constant temperature during the melting process is due to the latent heat of fusion, and only after melting, absorbed heat increases water's temperature.

Explanation:

The temperature of the water inside the beaker after all of the ice melts begins to increase. When ice is in the process of melting, it absorbs heat from its surroundings without a change in temperature, maintaining a temperature of 0°C until it has completely melted. This absorption of heat at a constant temperature is due to the latent heat of fusion, which is the energy required to change a substance from the solid phase to the liquid phase at constant temperature and pressure. Once all the ice has melted, any additional heat the water absorbs increases its temperature. This is due to the fact that the energy absorbed by the water is now used to increase the kinetic energy of the water molecules, resulting in a temperature increase.

Figure 10.26 illustrates this phenomenon with a beaker of ice starting at -12.0°C and gradually warming to 0°C as it absorbs heat. Initially, a small amount melts, but the overall temperature does not increase until all of the ice is melted. Only then does the temperature of the now liquid water begin to rise, eventually reaching 22.2°C due to continued heat absorption.

How do you calculate acceleration on a velocity time graph

Answers

Acceleration on a velocity time graph is found by calculating the change in the velocity over the change in time, or in other words, the slope. To do so, it's (final v-initial v)/(final t-initial t), where v is the velocity and t is time. Just find the final point you are looking for on the velocity time graph and determine its velocity and time. Then do the same for the initial point on the velocity time graph. Subtract the final velocity from the initial velocity and divide it by the final time minus the initial time and you will find the velocity for that interval. If you are looking for the instantaneous velocity at one specific point and not a interval, it's just the slope of the line at that point in time.

To calculate acceleration from a velocity-time graph, determine the slope of the graph at a specific point by dividing the change in velocity by the change in time.

To calculate acceleration from a velocity-time graph, you need to find the slope of the graph at a specific point. Acceleration represents the rate of change of velocity, and the slope of a graph represents the rate of change of the dependent variable with respect to the independent variable.

Here are the steps to calculate acceleration from a velocity-time graph:

Identify the specific point on the graph where you want to determine the acceleration.

Draw a tangent line to the curve at that point. The tangent line should touch the curve at only one point.

Measure the slope of the tangent line. You can do this by determining the change in velocity (Δv) and the change in time (Δt) between two points on the tangent line.

Calculate the acceleration by dividing the change in velocity by the change in time: acceleration (a) = Δv / Δt.

Note: If the velocity-time graph is a straight line, the acceleration is constant throughout, and you can calculate it by taking the slope of the line directly.

Remember that the units of acceleration will depend on the units used for velocity (e.g., meters per second, miles per hour) and time (e.g., seconds, minutes).

Therefore, Determine the slope of the graph at a certain point by dividing the change in velocity by the change in time in order to calculate acceleration from a velocity-time graph.

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Suppose you have 100kg of fresh strawberries. What would be the approximate mass of the strawberries after freeze-drying

Answers

I think it would be 10kg and removing water from food (freeze-drying) reduces it’s mass by 90% and 100-90=10 ..

The mass of strawberries after freeze-drying would be significantly less than their original mass, given that most of the water content is removed during the process. For 100 kg of fresh strawberries, the approximate mass after freeze-drying would be about 8.4 kg, assuming 91.6% water content.

The approximate mass of strawberries after freeze-drying can be calculated by considering the water content in the fresh strawberries. Fresh strawberries consist of about 91.6% water. During the freeze-drying process, most of this water is removed, hence reducing the mass significantly.

To estimate this change in mass, we can subtract the mass of water (91.6% of the original mass) from the total mass of the fresh strawberries (100 kg). Thus, the dried strawberries would approximately be 8.4% of their original mass, since the mass of fructose and other non-water components remain. This is an estimation and the actual number can be slightly higher or lower depending on the exact freeze-drying process and the specifics of the strawberries.

Therefore, after freeze-drying 100 kg of fresh strawberries, which originally consist of 91.6% water, the approximate mass of the strawberries would be about 8.4 kg.

A small dingy is floating up to a pirate’s ship full of would be boarders. He angles his cannon downward at -15 degrees while 3.0m above the water. He fires his cannon at 95 m/s. The small boat of unfortunate crewmen is 20 m away. Do they survive their foolhardy errand?(please show work)

Answers

Speed of the cannon is 95 m/s

now we will find its two components

speed in horizontal direction is

[tex]v_x = 95 cos15[/tex]

[tex]v_x = 91.76 m/s[/tex]

speed in vertical direction is

[tex]v_y = 95 sin(-15)[/tex]

[tex]v_y = -24.6 m/s[/tex]

now the time taken by the cannon to reach the water surface will be find out by using kinematics

[tex]\Delta y = v_y * t + \frac{1}{2} at^2[/tex]

[tex]-3 = -24.6 * t - \frac{1}{2}9.8 * t^2[/tex]

[tex]4.9t^2 + 24.6 t - 3 = 0[/tex]

By solving above quadratic equation

[tex]t = 0.12 s[/tex]

now in the same time the horizontal distance moved by the cannon

[tex]d_x = v_x * t[/tex]

[tex]d_x = 91.76 * 0.12[/tex]

[tex]d_x = 10.93 m[/tex]

Since the distance of crewmen is 20 m so it will definitely safe as cannon will hit at distance 10.93 m

In an attempt to reduce our dependence on non–renewable resources, and cut down on the harm to the environment, we could burn ______ to produce electricity.

Answers

In an attempt to reduce our dependence on non-renewable resources, and cut down on the harm to the environment, we could burn biomass to produce electricity.

The planets stay in orbit due to
A.kinetics
B.friction
C.gravity
D.mass

Answers

The planet stay in orbit due to gravity. because the gravity of the sun  keeps  the planets in their orbits,

Please help fast.

______ is a unit of speed.

A: m/s

B: min

C: m

D: km

Answers

A. m/s is a unit for speed.

Minutes, meters, and kilometers are incorrect.

Please brainliest me if this helped; trying to level up!

The unit for speed is meter per second ( m/s).  

Answer : Option A

Explanation:

The speed is the measure of the total distance traveled over a specified or particular time. Therefore, and as we know that the unit of distance is meter and that of time is seconds according to the S. I. unit of system. Therefore the unit of speed written as the meter per second, or, m / s, or, m s -1.

What effects can occur when heat energy is added to a system?

Select all that apply.

increase in temperature
decrease in temperature
change of state
phase change

Answers

Increase in temperature
Change of state
Phase change
Answer:

when heat energy is added to a system, change in system can be:

Increase in temperature: If system doesn't absorb the heat energy, then the effect will be increase in temperature.Change of state: If system absorbs the heat energy. And energy change in system can change the state of system.Phase change: If system absorbs the heat energy then the phase of system can be changed. For example liquid can be converted into vapors by adding heat energy to system.

Jim wants to learn more about the feeding habits of ants. What steps should he take in order to best study the patterns of ants?

Answers

They have any farm kits. You can observe the ants and their patterns for as long as you wish or at any time you wish keep a journal

Which data table describes the Sun? A. Composition mostly frozen nitrogen Mass 258.9 × 1018 kg B. Composition mostly hydrogen and helium gas Mass 1.989 × 1030 kg C. Composition fine dust, metals and minerals, and volcanic rock Mass 6.4 × 1023 kg D. Composition central iron core surrounded by rock, similar to Earth Mass 4.9 × 1024 kg

Answers

The Sun is a star around which our planet Earth and other planets and satellites of our solar system revolve along specific orbits. Sun appears to be spherical in shape and consists of glowing hot gases. It contains mostly hydrogen and helium gases. The temperature of the gas mixture is extremely high.

Therefore, the Sun mostly composed of hydrogen and helium gases.

(Answer) B. Composition mostly hydrogen and helium gas, Mass 1.989 x 10^30 Kg

1. California sea lions can swim as fast as 40.0 km/h. Suppose a sea lion begins to chase a fish at this speed when the fish is 60.0 m away. The fish, of course, does not wait, and swims away at a speed of 16.0 km/h. How long would it take the sea lion to catch the fish?
2. A pet-store supply truck moves at 25.0 m/s north along a highway. Inside, a dog moves at 1.75 m/s at an angle of 35.0° east of north. What is the velocity of the dog relative to the road?

Please explain your work and give the formulas you used. Tysm <3!

Answers

Answer:

1) time t = 9 s

2) velocity v  = 26.4 m/s 2.17° east of north

Explanation:

1

Given

velocity of sea lion [tex]v_s = 40.0 kmph[/tex]

velocity of the fish [tex]v-f = 16 kmph[/tex]

Distance  between the fish and sea lion d = 60 m

Solution

Relative velocity of the sea lion with respect to the fish

[tex]v = v_s - v_f\\\\v = 40 - 16\\\\v = 24.kmph\\\\v = 24 \times \frac{1000}{60 \times 60}  m/s\\\\v = 6.67 m/s[/tex]

Time

[tex]t = \frac{d}{v} \\\\t = \frac{60}{6.67} \\\\t = 9 s[/tex]

2

Given

velocity of the truck [tex]v_t = 25 m/s[/tex]

velocity of the dog [tex]v_d = 1.75 m/s[/tex]

Angle [tex]\theta = 35.0^o[/tex]

Solution

Dog moves in north east so

Component of velocity in East

[tex]v_{d,E} = v_dsin\theta\\\\v_{d,E} = 1.75 \times sin35\\\\v_{d,E} = 1.004 m/s[/tex]

Component of velocity in North

[tex]v_{d,N} = v_dcos\theta\\\\v_{d,N} = 1.75 \times cos35\\\\v_{d,N} = 1.434 m/s[/tex]

The velocity of Dog relative to the road = velocity of the dog relative to truck + velocity of the truck relative to the road

Y component

[tex]v_y = v_t + v_{d,N}\\\\v_y = 25 + 1.434\\\\v_y = 26.434 m/s[/tex]

X component

[tex]v_x = v_{d,E}\\\\V_x = 1.004 m/s[/tex]

Velocity

[tex]v = \sqrt{v_x^{2} +v_y^{2} } \\\\v = \sqrt{1.004^2 + 26.434^2} \\\\v = 26.4 m/s[/tex]

Direction

[tex]\phi = tan^{-1}\frac{v_x}{v_y} \\\\\phi = tan^{-1}\frac{1.004}{26.434} \\\\\phi = 2.17^o east of north[/tex]

For the time and velocity:

The sea lion will catch the fish in 0.42 seconds.

The velocity of the dog relative to the road is 26.41 m/s north.

How to find time and velocity?

Question 1: Formula:

Relative velocity = vA - vB

The sea lion is moving at a relative velocity of 40.0 - 16.0 = 24.0 km/h faster than the fish.

The distance between the sea lion and the fish is 60.0 m, which is 0.160 km.

The time it takes the sea lion to catch the fish is:

time = distance / relative velocity

= 0.160 km / 24.0 km/h

= 0.007 h

= 0.42 seconds

Therefore, it would take the sea lion 0.42 seconds to catch the fish.

Question 2: Formula:

Relative velocity = vA + vB

The velocity of the dog relative to the road can be found by adding the velocity of the truck and the velocity of the dog.

The velocity of the truck is 25.0 m/s north.

The velocity of the dog can be broken down into two components: a northward component of 1.75 × cos(35.0°) = 1.41 m/s and an eastward component of 1.75 × sin(35.0°) = 1.18 m/s.

Therefore, the velocity of the dog relative to the road is 25.0 + 1.41 = 26.41 m/s north.

The direction of the velocity of the dog relative to the road is north.

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Which quantity is a scalar quantity?
A.
acceleration
B.
area
C.
displacement
D.
force
E.
velocity

Answers

Area is the scalar quantity,

Answer:

The correct answer is option B.

Explanation:

Scalar quantity are those which only have magnitude and no direction.

For example:  mass, time, distance etc.

Vector quantity are those which have  both magnitude and direction.

For example:  displacement , velocity etc.

From the given options, the quantity which is scalar is are a because it only has magnitude but no directions.

Where acceleration, velocity, displacement  and force all are vector quantities.

Hence, the correct answer is option B.

what did bohr contribute to modern atomic theory

Answers

Bohr’s model showed that electron orbits had distinct radii.

Answer:

bohr developed a model of the atom that predicts how it will behave

Explanation:  

a p e x :)

Two carts (m= 0.4 kg each) are placed on an aluminum track. The first cart pushed with the initial velocity of 1.5 m/s towards the second cart, which remains at rest until the collision. Determine the velocities if both carts after the collision.

Answers

here two cars are placed on an aluminium track

so there is no friction on two carts during their motion and hence there is no external force on them

now if there is no external force so momentum is conserved

[tex]m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f][/tex]

here

[tex]m_1 = m_2 = 0.4 kg[/tex]

[tex]v_{1i} = 1.5 m/s[/tex]

[tex]v_{2i} = 0[/tex]

now plug in all values in it

[tex]0.4 * 1.5 + 0 = 0.4* v_{1f} + 0.4*v_{2f}[/tex]

divide whole equation by mass 0.4

[tex]v_{1f} + v_{2f} = 1.5[/tex]

also be the equation of coefficient of restitution

[tex]e = 1 = \frac{v_{2f} - v_{1f}}{v_{1i} - v_{2i}}[/tex]

now we have

[tex]v_{2f} - v_{1f} = 1.5[/tex]

now by solving above equations we will have

[tex]v_{2f} = 1.5 m/s[/tex]

[tex]v_{1f} = 0[/tex]

so after collision speed of two carts is 0 m/s and 1.5 m/s after collision

How to get displacement

Answers

Displacement is how much of a liquid (typically water for simplicity in the metric system) is pushed aside when another object is completely submerged. For example, when a 100mL of water has a block placed into it, and rises to 150mL, the block has displaced the water.

what did bohr contribute to modern atomic theory

Answers

He created an atomic model and Bohr diagram, if that could be it.

Answer:

Bohr atomic model

Explanation:

Bohr's atomic model:

Bohr's atomic model was proposed by Neil Bohr in 1913. In this atomic model  Neil Bohr's modified the Rutherford Model and show how electrons in an atoms moves around the nucleus in stable orbits. According to Rutherford model electron's in atoms are filled in orbits and these electron moves around the nucleus in these orbits like planets moves around the sun in fixed orbit but Rutherford's model was unable to show the stability of orbits. To solve this problem, Bohr proposed a new model b. According to this model electrons move around the nucleus in fixed size orbits which have fixed energy and the electron with low energy is filled in smaller size orbit. Radiation are emitted from atoms only when transition of electron from higher energy orbit to lower energy orbit takes place.

A friction force of 280 N exists between a cart and the path. If the force of reaction is 766 N, what is the minimum action force needed to set the cart in motion?

Answers

force of friction on the cart is given as

[tex]F_f = 280 N[/tex]

here we also know the reaction force due to surface

[tex]R = 766 N[/tex]

so we can say reaction force is given as

[tex]R = \sqrt{F_n^2 + F_f^2}[/tex]

[tex]766 = \sqrt{F_n^2 + 280^2}[/tex]

[tex]F_n^2 = 766^2 - 280^2[/tex]

[tex]F_n = 713 N[/tex]

now by force balance we will say

[tex]F_y + F_n = mg[/tex]

[tex]F_y = mg - F_n[/tex]

[tex]F_x = F_f[/tex]

also we know that

[tex]F_f = \mu * F_n[/tex]

[tex]280 = \mu * 713[/tex]

[tex]\mu = 0.39[/tex]

now minimum force required to set this into motion

[tex]F_{min} = \frac{\mu mg}{\sqrt{1 + \mu^2}}[/tex]

here we know that

[tex]mg = F_n = 713 N[/tex]

[tex]F_{min} = \frac{0.39* 713}{\sqrt{1 + 0.39^2}}[/tex]

[tex]F_{min} = 259 N[/tex]

So it will require 259 N minimum force to move it

Carbon (C) and hydrogen (H) are pure substances. Each is made of only one type of atom, but carbon atoms are different from hydrogen atoms. Carbon and hydrogen chemically combine to form methane (CH4).

Based on this information,


A.
carbon, hydrogen, and methane are all compounds.
B.
methane is an element and carbon and hydrogen are compounds.
C.
carbon and hydrogen are elements and methane is a compound.
D.
carbon, hydrogen, and methane are all elements.

Answers

C.  

carbon and hydrogen are elements and methane is a compound.

Answer:

C. carbon and hydrogen are elements and methane is a compound.

Explanation:

Elements are substances which have one type of atoms. Compounds are substances which have different types of atoms. Since, Carbon and Methane have only one type of atoms and thus, these are pure substances. Methane  contains atoms of Carbon and Hydrogen chemically combined together. Thus, methane is a compound.

Why is it important to balance a chemical equation?

A. It is not important to balance a chemical equal
B. To make sure you have the correct products
C. To make sure you have the correct reactants
D. To obey the law of conservation of mass

Answers

The chemical equation of a chemical must be balanced to obey the law of conservation of mass. Therefore, option (D) is correct.

What is the balanced chemical equation?

The equation in which the number of atoms of each element of reactants is equal to the number of atoms of each element of products is called a balanced chemical equation.

The law of conservation of mass obeys by a balancing of a chemical equation for a chemical reaction. According to this law, the mass of matter can neither be created nor be destroyed in a chemical reaction.

By following this law, the total mass of the elements on the reactant side should be equal to the total mass of elements on the product side in a balanced chemical equation.

An example of the balanced chemical equation is the formation of water:

2H₂ + O₂  →  2H₂O

On both sides of the arrow in the equation, the number of hydrogen and oxygen atoms is equal and so are their masses. Therefore this chemical equation obeys the law of conservation of mass.

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What is the purpose of mucilage in the spaces around the cells of hornworts? Why is this important?

Answers

Final answer:

The mucilage in hornwort cells is crucial for maintaining water balance, protecting the plant from drying, aiding in nutrient capturing, and promoting bacterial interaction. It ensures the plant's survival and growth prospects in various environments.

Explanation:

The mucilage in the spaces around the cells of hornworts serves a critical role in maintaining the plant's water balance and protecting it from drying out. It does this by absorbing water and creating a moist environment that helps in preventing water loss via transpiration. Additionally, the mucilage also aids in nutrient capturing and bacterial interaction that promotes the growth of the plant.

This is extremely important as it not only improves the plant's survival rate in various environments but also allows the plant to photosynthesize effectively, and thus, grow and propagate successfully. So, understanding the role of mucilage in hornworts is crucial for their conservation and in understanding plant adaptation mechanisms in general.

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Mucilage in hornwort cells stabilizes water content, ensuring hydration, and binds pathogens to protect against infections. It also improves root-soil contact, enhancing nutrient and water absorption. These functions are essential for the hornwort's survival and growth.

The mucilage in the spaces around the cells of hornworts plays several critical roles. Firstly, it helps to stabilize the water content of the surrounding environment, ensuring that the hornwort cells remain hydrated even during dry conditions. This is crucial for the plant's survival and growth. Additionally, the mucilage helps to bind pathogens, protecting the cells from potential infections. This dual role of maintaining hydration and offering protection is essential for the overall health and longevity of the hornwort.

Moreover, mucilage improves the contact between the root and soil, preventing gaps which would drastically reduce the absorption of water and nutrients. Additionally, the mucilage's high water content and resistance to proteolysis due to its extensive mucosylation make it an effective barrier and stabilizer in various environmental conditions.

wich of the folling is best definition of vectors (quantities described by both force and gravity)(quantities described by bothspeed amnd movement)(quantities described by both velocity and acceleration)(quantities described by both magnitud)

Answers

Answer:

Option D is quantities described by both magnitude and direction is the correct answer.

Explanation:

A scalar is quantity with magnitude only. It does not have direction. Examples of scalar are distance, speed, time etc.

A vector is quantity with both magnitude and direction. Some examples for vectors are displacement, velocity, acceleration, force, moment, electric field, magnetic field etc.

Here option A, quantities described by both force and gravity is not correct.

Option B is quantities described by both speed and movement is also not correct.

Option C is quantities described by both velocity and acceleration is also not correct.

Option D is quantities described by both magnitude and direction is the correct answer.

How much would a 70.0-kg person weigh on Mercury?

Answers

AS Weight = w =mg

          m= 70kg

 g on mercury =3.7 m/s²

so  W = (70kg) ( 3.7m/s²)

      w=259 kgm/s²

w = 259 N

A sealed container filled with gas is heated. What happens?

The gas escapes

The movement of the molecules slows

The internal pressure decreases

The internal pressure increases

Answers

The internal pressure increases as the gas is heated

The internal pressure increases

During a crash test, an air bag inflates to stop a dummy’s forward motion. The dummy’s mass is 75kg. If the net force on the dummy is 825 N toward the rear of the car, what is the dummy’s acceleration?

Answers

Mass of the dummy m = 75 kg

Net Force on the dummy [tex]F_{net}  = -825 N[/tex] since it is given that the force is towards the backside of the car.

Acceleration of the dummy a = ?

Using Newton's 2nd law of motion, we have

[tex]F_{net}  = ma[/tex]

-825 = (75)a

Hence, [tex]a =  \frac{-825}{75}[/tex]

Acceleration of the dummy is -11 [tex]m/s^{2}[/tex]

The negative sign indicates that the dummy is slowing at a rate of 11 [tex]m/s^{2}[/tex]

Answer:

        Acceleration towards rear = 11 [tex]m/s^2[/tex]

        Acceleration towards direction of movement of dummy  = -11 [tex]m/s^2[/tex]

Explanation:

  Mass of dummy = 75 kg

   Force acted towards rear of the car = 825 N

   We have Force acting on a body = Mass of body * Acceleration of body

   Substituting the given values in the above equation we will get

        825  = 75 * a

         a = 11 [tex]m/s^2[/tex]

        So acceleration towards rear = 11 [tex]m/s^2[/tex]

        Acceleration towards direction of movement of dummy  = -11 [tex]m/s^2[/tex]

A metal ball of mass 2 kg is supported by a massless inextensible string, 12 cm long. A

horizontal force displaces the ball by 30o

to the vertical so that the string remains taut. Find:

a) the horizontal force.

b) the tension in the thread.

Answers

(a) the horizontal force is 11.3 N

(b) The tension in the thread is 22.6 N

Draw a free body diagram for the suspended metal ball as shown in the figure. The tension T acts along the length of the thread, the force F is the horizontal force and its weight is mg, which acts vertically down wards.

Resolve the tension into two components- T cos 30 along the vertical and T sin30 along the horizontal as shown in the figure.

Apply the condition for equilibrium along the horizontal direction.

[tex]F=Tsin30........(1)[/tex]

Apply the condition for equilibrium along the vertical direction.

[tex]mg=Tcos30.......(2)[/tex]

Divide equation (1) by equation (2) and write an expression for F.

[tex]\frac{F}{mg} = tan30\\ F=mgtan30[/tex]

Substitute 2 kg for m and 9.81 m/s² for g.

[tex]F=mgtan30\\ =(2kg)(9.81m/s^2)(tan30^o)\\ =11.3N[/tex]

The horizontal force required to keep the ball taut is 11.3 N

From equation (2),

[tex]T=\frac{mg}{sin30} \\ =\frac{(2kg)(9.81m/s^2)}{sin30^o} \\ =22.6N[/tex]

Thus, the tension in the thread is 22.6 N

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