How high will a

rock go if thrown right up by someone that does
of work-related on it? ignore air resistance.

You are watching: When the speed of your car is doubled, by what factor does its kinetic energy increase?

Explanation:

Known

Unknown

When other does work-related on an item it transforms the complete energy that the object. In this case, the work-related done by the human being converts to kinetic power as the rock is launched. This kinetic energy is climate turned right into gravitational potential energy when the stone is in ~ the highest allude of the peak.

Work done = Kinetic energy when the stone leaves the hand = Gravitational Potential energy at the peak

We can collection the work-related done to the gravitational potential energy

Plug in our known values and solve.

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### Example inquiry #2 : types Of Mechanical power

car rolling top top a horizontal road has actually speed of
as soon as it strikes a horizontal coiled spring and also is lugged to rest in a distance of
. What is the spring stiffness continuous of the spring?

Explanation:

Known

We need to transform our velocity to

Unkonwn

The easiest method to fix this difficulty is with conservation the energy. As soon as the automobile is rolling follow me the roadway it has actually kinetic energy. When the spring brings it come a complete stop, the auto has elastic potential energy. Follow to the regulation of preservation of energy, these two values must be equal to one another

We deserve to now plug in our known values and also solve because that the missing variable

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### Example question #3 : varieties Of Mechanical energy

sphere is around to role off the leaf of a
high table. What is its existing potential energy?

Explanation:

The equation for potential energy is

. Us are offered the mass of the ball, the height of the table, and also the acceleration of heaviness in the question. The distance the sphere travels is in the bottom direction, making the negative.

Plug in the values, and solve for the potential energy.

The units for power are Joules.

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### Example concern #4 : varieties Of Mechanical energy

A spring has a spring stiffness constant of

. Just how much should this spring be stretched to store
that potential energy?

Explanation:

Knowns

Unknowns

Equation

Plug in the vales and solve for the stretch the the spring.

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### Example concern #5 : types Of Mechanical power

A car traveling at a velocity

can stop in a minimum street
. What would be the car’s minimum protecting against distance if it to be traveling at a velocity of
?

Explanation:

Work causes a adjust in the kinetic power of an object. In the example of a vehicle stopping, the work done on the automobile causes the auto to slow down to a stop, therefore changing the kinetic energy.

Work is additionally equal to the force times the displacement of the object. In this case, we are assuming that the force applied to avoid the auto does no change.

Since the car is comes to a avoid the final velocity of the car is 0m/s.

Therefore once you twin the velocity, that worth is then squared.

Therefore your kinetic energy is boosted by

time the original amount.

time greater, than v the same pressure being applied, the preventing distance will likewise increase by
times since they are directly related.

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### Example inquiry #6 : types Of Mechanical power

massive attached come the end of a spring reasons it come stretch
. If another
massive is added to the spring, the potential power of the spring will be

Twice together much

The same

3 times together much

4 times as much

Twice together much

Explanation:

Hooke’s law states the spring continuous is directly related to the force applied and also the distance that the thing is stretched.

We also know that the potential energy of a feather is regarded the spring consistent and the street that the thing is stretched

We have the right to substitute our equation because that Hooke’s law into the potential power equation.

This simplifies to

This equation mirrors that over there is a straight relationship between the force on the spring and also the potential power of the spring. If the pressure is doubled, then the potential energy will similarly double.

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### Example question #7 : types Of Mechanical power

A feather with

hangs vertically alongside a ruler. The end of the feather is next to the
note on the ruler. If a
fixed is currently attached to the end of the spring, whereby will the end of the feather line up through the ruler marks?

Explanation:

Known

Unknown

First let us think about the pressure acting ~ above the spring. Because the spring is hanging vertically, the only force acting ~ above the feather is the force of heaviness from the fixed that has been added to the spring.

We deserve to substitute in ours variables and also find the gravitational force.

According to Hooke’s regulation the spring continuous of a spring is directly proportional to the pressure acting top top it and also inversely proportional come the quantity of stretch.

We deserve to use the noted spring consistent and the force acting on the spring to determine the amount of stretch.

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### Example inquiry #8 : species Of Mechanical power

A baseball has a fixed of

. If a high institution pitcher can throw a baseball at
, what is the approximate kinetic energy connected with this pitch?

Explanation:

To solve for the kinetic energy, we will have to use the equation:

Before we have the right to plug in our provided values, us must transform the mass indigenous grams come kilograms. Remember, the SI unit for mass is kilograms, so most calculations will need this conversion.

Now we deserve to use this mass and the offered velocity to fix for the kinetic energy.

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### Example question #9 : types Of Mechanical energy

When the rate of your car is doubled, by what element does that is kinetic power increase?

Explanation:

Therefore when you double the velocity, that worth is climate squared.

Therefore her kinetic power is boosted by 4 time the initial amount.

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