To test the impact performance of a 10 cm thick gymnastics mat, a 20 kg cylindrical
mass is dropped onto the mat from a height of 1 m above the mat. During the impact,
the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to
only 4 cm thick.

a. How much kinetic energy does the cylinder have at the instant just before it
contacts the mat?

b. How much work does the mat do to stop the fall of the cylinder?

c. What average vertical force does the mat exert on the cylinder during the impact,
from contact until the cylinder’s vertical velocity is zero?

Answers

Answer 1

Answer:

A)196J

B)-208J

C)3467J

Step-by-step explanation:

We are given that a 20 kg cylindrical  mass is dropped onto the mat from a height of 1 m above the mat. During the impact,  the cylinder’s vertical velocity reaches zero at the instant the mat has compressed to  only 4 cm thick.

So, The Mat gets compressed by : 10cm - 4 cm = 6 cm=0.06 m

a)

Using Conservations of energy

Potential energy at the top = Kinetic energy at the point before touching the surface

Kinetic energy = mgh= [tex]20 \times 9.8 \times 1 = 196 J[/tex]

b)

Work done  by the mat do to stop the fall of the cylinder =[tex]-mg(h+0.06)=-20 \times 9.8(1+0.06)=-208 J[/tex]

C)

Work done=[tex]\text{Average force} \times \text{ Compression of mat}[/tex]

[tex]208=F \times 0.06[/tex]

F=3467J


Related Questions

please help me with this and show work thank you!!

Answers

[tex]21x^{2} -16x^{2} = 5x^{2} \\-18x-9x=-27x\\4-8=-4\\25x^{3} +5x^{2} -27x-4\\A[/tex]

find the area of the figure

Answers

Answer:

121π or ≈380.13

Step-by-step explanation:

Area of a circle = πr²

A = π(11)²

A = 121π or A ≈ 380.13

PLEASE HELP. I HAVE LIMITED TIME.

5. X to the fourth power plus the product of six and the square root of nine.
6. Fifteen plus eight cubed minus the sum of fourteen and six squared.
7. The product of three and fifteen minus nine plus the quotient of fifteen and three.
8. The product of seventeen and y, plus the square root of eighty-one minus the product of six and x minus four.

Answers

i think this is it, but i’m not sure about the last one

Find the volume of a right circular cone that has a height of 13 in and a base with a
circumference of 5.1 in. Round your answer to the nearest tenth of a cubic inch.

Answers

Answer:

Step-by-step explanation:

the formula for finding  the volume of a cone would be V= 3.14 r sqaured * h/3

so plug that in and it would be   3.14(5.1) sqaured * 13/3

3.14 is the formula of pie which is in the formula for finding the volume of

5.1*5.1=  26.01

3.14* 26.01= 81.67    

13/3= 4.34

81.67* 4.34= 354.45

The volume of a right circular cone that has a height of 13 in and a base with a circumference of 5.1 inches is 8.97824.

Calculation of the volume of right circular cone:

Since

We know that

Volume = [tex]\pi r^2 \frac{h}{3}[/tex]

Since the circumference is 5.1 inches

So here the radius be like

Circumference = [tex]2\pi r[/tex]

5.1 = 2(3.14) r

r = 0.8121

Now the volume should be

[tex]= 3.14 \times (0.8121)^2 \frac{13}{3}[/tex]

= 8.97824

Hence, The volume of a right circular cone that has a height of 13 in and a base with a circumference of 5.1 inches is 8.97824.

Learn more about volume here: https://brainly.com/question/24420115

image attached below​

Answers

Answer:

1) Expression

2) Equation

3) Equation

4) Expression

Step-by-step explanation:

An equation always contains an equal sign, so in this case, if it doesn't contain an equal sign, it's an expression.

For 2 and 3, you can see that there is an equal sign, but for 1 and 4, there is not.

Therefore, 1 and 4 are expressions and 2 and 3 are equations.

I hope this helped.

5x+2(x+3) is an expression

5x=2(x+3) is an equation

8m-3m+5=16 is an equation

8m-3m+5-16 is an expression

An equation always and I mean ALWAYS uses a = sign.

An expression is a combination of numbers and variables and symbols.

Hope that's useful

Select all the values that make the inequality true n<-15
A. -25
B. -1
C. -30
D. -19

Answers

The answers are A, C, and D. Because they are all furthest from 0 on a number line.

In a quiz, positive marks are given for correct answers and
negative marks are given for incorrect answers. If Jack ‘s scores
in five successive rounds were 25, -5, -10,15 and 10, what was his
total at the end?

Answers

Answer:

35

Step-by-step explanation:

just trust me its the total

Answer:

35

Step-by-step explanation:

25-5=20

20-10=10

10+15=25

25+10=35

There must be at least 20 club members present in order to hold a meeting.​

Answers

Answer:

Are you trying to create a meeting?

Step-by-step explanation:

If u are i can help? :)

x (number of members) is larger or equal to 20

Which of the following shows an example of the identity property of 0? Select one: a. 1/2+1/2=1 b. 22/7+(-22/7)=0 c. 0+(-7 5/6)=-7 5/6 d. -3 1/4+6 1/2=3 1/4

Answers

I believe the answer is C
Hope this helps

The  example of the identity property of 0 will be 0 + (–7 5/6) = –7 5/6. Then the correct option is C.

What is identity property of addition?

According to the identity property of addition, any value is that summation of 0 and any other value.

a + 0 = a

The  example of the identity property of 0 will be

0 + (–7 5/6) = –7 5/6

Then the correct option is C.

More about the identity property of addition link is given below.

https://brainly.com/question/1709448

#SPJ2

The area of a square is given by A= s2 where s is the length of each side of the square if the area of a square room is 64 square meters what is the length of 1 side of the room in meters

Answers

9514 1404 393

Answer:

  8 m

Step-by-step explanation:

Using the given information, we know that ...

  64 m^2 = A = s^2

  (8 m)^2 = s^2

  8 m = s

The length of one side of the room is 8 meters.

2548 rounded to thousand

Answers

Answer:

3000

Step-by-step explanation:

The world’s largest sign for Coca-Cola is located in Arica, Chile. The rectangular sign has a length of 400 feet and has an area of 52,400 square feet. Find the width of the sign. (Show work please!)

Answers

Answer:

131 feet

Step-by-step explanation:

52,400/400 = 131 ft

A pot of stew is placed on a stove to heat. The temperature of the liquid reaches 170°F, and then the pot is taken off the burner and placed on a kitchen counter. The temperature of the air in the kitchen is 76°F.
If k = 0.34, the temperature of the liquid after 7 hours will be

Answers

Answer:

Step-by-step explanation:

scvghytredfvbghnju7y6tg

Mary earns $7.25 an hour. She can determine her salary, s, for the
number of hours she works, h, by using the equation s = 7.25h. Which
statement explains why s is a function of h?
A
For every value of h there is only one value of s.
B.
For some values of h there is more than one value of s.
C.
For some values of s there is more than one value of h.
For every value of s there are two values of h.
D.

Answers

Answer: A

I’m pretty sure I’m sorry if I’m wrong

Please help if you know how to do this, thanks

Answers

9514 1404 393

Answer:

  1.  see the first attachment for a graph; quadrants I, II, III; vertex (-3, -4); x-intercepts -5, -1; graph is dashed line, shaded inside the parabola, which opens up

  2.  see the second attachment for a graph; all quadrants; vertex (1, 2); x-intercepts 1±√2; graph is a solid line, shaded outside the parabola, which opens down; (-7, 0) is a solution

Step-by-step explanation:

1. The boundary expression is in vertex form, so the vertex can be read directly.

  y = (x -h)^2 +k . . . . . . parabola with vertex (h, k)

  y > (x +3)^2 -4 . . . . .  (h, k) = (-3, -4)

The leading coefficient is +1, a positive number, so the parabola opens up. The relation is y > ( ), so values of y above the dashed line will be shaded. Those values are inside the parabola. The points (0, 0) and (-7, 0) are not in the shaded area, so are not solutions.

__

2. Again, the boundary expression is in vertex form, so the vertex can be read directly.

  y ≥ -(x -1)^2 +2 . . . . . (h, k) = (1, 2)

The x-intercepts are found by solving for x when y=0:

  0 = -(x -1)^2 +2

  x -1 = ±√2

  x = 1±√2

The leading coefficient is -1, so the parabola opens downward. The relation is y ≥ ( ), so y-values above the solid line will be shaded. Those values are outside the parabola. Point (0, 0) is not a solution. Point (-7, 0) is a solution.

_____

Additional comment

As with the graph of any inequality, the boundary line is solid when the "or equal to" case is part of the relation. If the relation is strictly "greater than" or "less than", then the boundary line is dashed.

Need Help please i will mark brainliest when it lets me

Answers

Answer:it’s the second one

Step-by-step explanation:

Answer:

the 2nd one

Step-by-step explanation:

I asked my brother and he said it was that one

help me out please i need help with this​

Answers

Answer:

8

Step-by-step explanation:

36/4.5

Answer: 8

4 1/2 = 4.50

36 divided by 4.50 = 8

Find perimeter of the figure :)

Answers

Answer:

39 feet.

Perimeter is the distance around a shape. To solve for it, we must add all the values together.

[tex]3 + 8 + 7 + 11 + 10 = 39[/tex]

If you need me to explain more, let me know.

In 2010, the average finishing time for marathons across the US was approximately 278 minutes, with a standard deviation of approximately 63 minutes. What finishing time defines the fastest 7.93% of runners?

Answers

Answer:

336 minutes

Step-by-step explanation:

Mean finishing time: 278 minutes

Standard Deviation: 63 minutes

Confidence interval: [278 - 63] , [278 + 63]  = [215 , 341] minutes

What finishing time defines the fastest 7.93% of runners?

This means the 7.93% of time closest to the upper limit of 341 minutes

341 - 215  ≡  63 × 2  = 126

7.93% of 126  = 0.0793 × 126  = 9.9918

341 - 9.9918 = 331.0082

Hence the finishing time that defines the fastest 7.93% of runners has an interval of [331 , 341] minutes with a mean or average of 336.0041 ≅ 336 minutes

What is 1+1. I keep on getting it wrong.

Answers

Answer:

11 duh

Step-by-step explanation:

Which graph shows the solution to this system of inequalities? 3x - y < 5 and x + y > 2( PLEASE HELP!! )

Answers

Answer:

D

Step-by-step explanation:

Just graph both inequalities and plug in 0 to see which way it goes.

Point N is on line segment MO. Given NO = 14 and MO = 18, determine the length MN.

Answers

4 because 18(MO)-14(NO)=4(MN)

Evaluate the function: f(n) = n + 4
Find: f(-9)
Evaluate the function

Answers

For this you just substitute -9 for n.

(-9)+4= -5

F(-9)=-5

express 60 As the product
of its prime
factors. Write
the prime factors in assessing
Order
ane give your
Answer index form

Answers

Given parameters:

 Number 60;

Problem;

Express as a product of its prime factors

Solution

Every number known can be expressed as a product of its prime factors. Prime factorization involves finding the prime numbers that when multiplied will give the true number.

Prime numbers are numbers that are products of 1 and itself only.

   For the number 60;

                      60  =   2 x 30

                             = 2 x 2 x 15

                             = 2 x 2 x 3 x 5

In index form;   2² x 3 x 5

 

Which expression has a value of 3/4

Answers

What are the expressions?

I WILL GIVE BRAINLEIST PLEASE HELP



The height of a golf ball hit in the air is modeled by the equation ℎ(t)=−16t2 + 48t, where ℎ(t) represents

the height, in feet, and t represents the number of seconds that have passed since the ball was hit.

Complete the statement about the function for ℎ(2)=32

If ℎ(2)=32 , then the ball reached a height of _________ feet after _________ seconds.

Answers

Answer:

16 feet, 2 seconds

Step-by-step explanation:

as the problem state that h= height and t = time, to get the h you need to isolate it so we divide it by 2 and we get 16 feet. The 2 are already in the problem h(2).

1.) x – 12.06 = -9.4
plz help

Answers

Here’s a step by step so you know for next time!

To easily find it you would simply switch around the equation, so instead of doing x-12.06=-9.4 just do -9.4+12.06 (the opposite of subtracting) which equals 2.66. And just to make sure I was correct I plugged it in, and the equation 2.66-12.06=-9.4 is correct.

Answer: x= 2.66

the sum of the measures of the angles of the interior angles of a triangle is 180. Write and solve an equation to find the value of the variable

Answers

Answer:

look on khan academy

Step-by-step explanation:

The perimeter of a triangle is 95 centimeters. If two sides are equally long and the third side is 5 centimeters longer than the others, find the lengths of
the three sides?

The length of each of the two equal sides is ____centimeters

Answers

Answer:

  [Let x = length of Side 1]

            ["two sides are equally long"]

            ["third side is 7cm longer than each of the others" (note edit)]

            ["perimeter of a triangle is 82 centimeters"]

Step-by-step explanation:

Red = R, Orange = O, Yellow = Y, etc; ALL CAPS

Answers

Answer:

I don't know what your asking, but if your asking about colors here you go.

Step-by-step explanation:

Green = G

Blue = B

Black = BL

Yellow = Y

Orange = O

Grey = GR

Purple = P

Red = R

Pink = PI

Thats all that I can think of right now

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