An electric hoist does 56,447 J of work in raising 115 kg load. How high (in meters) was the load lifted?

How fast must an object move before its length appears to be contracted to one-fourth its proper length? (Give your answer in te

Tresset [83]

Answer:

0.97c

Explanation:

From the relativistic equation for length contraction, we have

$l$ = $l_{0}\sqrt{1 - \beta }$

where

$l$ is the final length of the object

$l_{0}$ is the original length of the object before contraction

β = $v^{2} /c^2$

where v is the speed of the object

c is the speed of light in free space = 3 x 10^8 m/s

The equation can be re-written as

$l$ / $l_{0}$ = $\sqrt{1 - \beta }$

For the length to contract to one-fourth of the proper length, then

$l$ / $l_{0}$ = 1/4

substituting into the equation, we'll have

1/4 = $\sqrt{1 - \beta }$

substituting for β, we'll have

1/4 = $\sqrt{1 - v^2/c^2 }$

squaring both side of the equation, we'll have

1/16 = 1 - $v^2/c^2$

$v^2/c^2$ = 1 - 1/16

$v^2/c^2$ = 15/16

square root both sides of the equation, we have

v/c = 0.968

v = 0.97c

3 0

3 years ago

calculate the mass of potassium chlorate (kcio3) required to obtain 10g of oxygen in the following reaction:kclO3-kcl+O2

igor_vitrenko [27]

First, balance the reaction:

_ KClO₃ ==> _ KCl + _ O₂

As is, there are 3 O's on the left and 2 O's on the right, so there needs to be a 2:3 ratio of KClO₃ to O₂. Then there are 2 K's and 2 Cl's among the reactants, so we have a 1:1 ratio of KClO₃ to KCl :

2 KClO₃ ==> 2 KCl + 3 O₂

Since we start with a known quantity of O₂, let's divide each coefficient by 3.

2/3 KClO₃ ==> 2/3 KCl + O₂

Next, look up the molar masses of each element involved:

• K: 39.0983 g/mol

• Cl: 35.453 g/mol

• O: 15.999 g/mol

Convert 10 g of O₂ to moles:

(10 g) / (31.998 g/mol) ≈ 0.31252 mol

The balanced reaction shows that we need 2/3 mol KClO₃ for every mole of O₂. So to produce 10 g of O₂, we need

(2/3 (mol KClO₃)/(mol O₂)) × (0.31252 mol O₂) ≈ 0.20835 mol KClO₃

KClO₃ has a total molar mass of about 122.549 g/mol. Then the reaction requires a mass of

(0.20835 mol) × (122.549 g/mol) ≈ 25.532 g

of KClO₃.

7 0

2 years ago

What are the rules for setting up an integral of rotation?

Angelina_Jolie [31]

Setting up an integral of rotation is used as a method of of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is similar to finding the area, but there is one additional component of rotating the area around a line of symmetry.

First the solid of revolution should be defined. The general function is y=f(x), on an interval [a,b].

Then the curve is rotated about a given axis to get the surface of the solid of revolution. That is the integral of the function.

It all depends of the function f(x), which must be known in order to calculate the integral.

3 0

2 years ago

Match each form of Energy with it's definition. Energy of motion Question 7 options: mechanical energy kinetic energy chemical e

Komok [63]

Answer:

a fireplace or burn gasoline in a car's engine.

Mechanical energy is energy stored in objects by tension. Compressed springs and stretched rubber bands are examples of stored mechanical energy.

Nuclear energy is energy stored in the nucleus of an atom—the energy that holds the nucleus together. Large amounts of energy can be released when the nuclei are combined or split apart.

Gravitational energy is energy stored in an object's height. The higher and heavier the object, the more gravitational energy is stored. When a person rides a bicycle down a steep hill and picks up speed, the gravitational energy is converting to motion energy. Hydropower is another example of gravitational energy, where gravity forces water down through a hydroelectric turbine to produce electricity.

Kinetic energy

Kinetic energy is the motion of waves, electrons, atoms, molecules, substances, and objects.

Radiant energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays, and radio waves. Light is one type of radiant energy. Sunshine is radiant energy, which provides the fuel and warmth that make life on earth possible.

Thermal energy, or heat, is the energy that comes from the movement of atoms and molecules in a substance. Heat increases when these particles move faster. Geothermal energy is the thermal energy in the earth.

Motion energy is energy stored in the movement of objects. The faster they move, the more energy is stored. It takes energy to get an object moving, and energy is released when an object slows down. Wind is an example of motion energy. A dramatic example of motion energy is a car crash—a car comes to a total stop and releases all of its motion energy at once in an uncontrolled instant.

Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. Sound is produced when a force causes an object or substance to vibrate. The energy is transferred through the substance in a wave. Typically, the energy in sound is smaller than in other forms of energy.

Electrical energy is delivered by tiny charged particles called electrons, typically moving through a wire. Lightning is an example of electrical energy in nature.

7 0

2 years ago

In a laboratory, it is often convenient to make measurements in centimeters and grams, but SI units are needed for calculations.

zheka24 [161]

Answer:

(a) 0.92 cm= 0.092 m.

(b) 141.64 g=0.14164 kg.

(c) 15. 8 cm³=0.0000158 m³

(d) 63.6 g/cm³= 63600 kg/m³

Explanation:

The International System of Units, abbreviated S.I., also called the International System of Measurements is a system of measurements in which its units are based on fundamental physical phenomena. The units of the S.I. They are the international reference for the indications of all measuring instruments.

The International System of Units (SI) arose from the need to unify and give coherence to a great variety of unit subsystems.

The International System of Units consists of seven basic units, also called fundamental units, which define the corresponding fundamental physical quantities and which allow any physical quantity to be expressed in terms or as a combination of them. The fundamental physical quantities are complemented by two more physical quantities, called supplementary ones.

By combining the basic units, the other units are obtained, called units derived from the International System, and which allow defining any physical quantity.

(a) The SI unit of length is the meter. Being 1 cm = 0.01 m, then 0.92 cm= 0.092 m.

(b) The SI unit of mass is kg. Being 1 g = 0.001 kg, then 141.64 g=0.14164 kg.

(c) Being 1 cm³ = 0.000001 m³, then 15. 8 cm³=0.0000158 m³

(d) Being 1 g/cm³= 1000 kg/m³, then 63.6 g/cm³= 63600 kg/m³

3 0

3 years ago