A metal block of mass 3 kg is falling downward and has velocity of 0.44 m/s when it is 0.8 m above the floor. It strikes the top of a relaxed vertical spring of length 0.4 m. The spring constant is 2000 N/m. After striking the spring, the block rebounds. What is the maximum height above the floor that the block reaches after the impact

Answers

Answer 1

Answer:

Answer:

$y_(max) = 0.829\,m$

Explanation:

Let assume that one end of the spring is attached to the ground. The speed of the metal block when hits the relaxed vertical spring is:

$v = \sqrt{(0.8\,(m)/(s))^(2) + 2\cdot (9.807\,(m)/(s^(2)) )\cdot (0.4\,m)}$

$v = 2.913\,(m)/(s)$

The maximum compression of the spring is calculated by using the Principle of Energy Conservation:

$(3\,kg)\cdot (9.807\,(m)/(s^(2)))\cdot (0.4\,m) + (1)/(2)\cdot (3\,kg)\cdot (2.913\,(m)/(s) )^(2) = (3\,kg) \cdot (9.807\,(m)/(s^(2)))\cdot (0.4\,m-\Delta s) + (1)/(2)\cdot (2000\,(N)/(m))\cdot (\Delta s) ^(2)$

After some algebraic handling, a second-order polynomial is formed:

$12.728\,J = (1)/(2)\cdot (2000\,(N)/(m) )\cdot (\Delta s)^(2) - (3\,kg)\cdot (9.807\,(m)/(s^(2)) )\cdot \Delta s$

$1000\cdot (\Delta s)^(2)-29.421\cdot \Delta s - 12.728 = 0$

The roots of the polynomial are, respectively:

$\Delta s_(1) \approx 0.128\,m$

$\Delta s_(2) \approx -0.099\,m$

The first root is the only solution that is physically reasonable. Then, the elongation of the spring is:

$\Delta s \approx 0.128\,m$

The maximum height that the block reaches after rebound is:

$(3\,kg) \cdot (9.807\,(m)/(s^(2)) )\cdot (0.4\,m-\Delta s) + (1)/(2)\cdot (2000\,(N)/(m))\cdot (\Delta s)^(2) = (3\,kg)\cdot (9.807\,(m)/(s^(2)) )\cdot y_(max)$

$y_(max) = 0.829\,m$

Answer 2

Answer:

Answer:

0.81 m

Explanation:

In all moment, the total energy is constant:

Energy of sistem = kinetics energy + potencial energy = CONSTANT

So, it doesn't matter what happens when the block hit the spring, what matters are the (1) and (2) states:

(1): metal block to 0.8 m above the floor

(2): metal block above the floor, with zero velocity ( how high, is the X)

Then:

$E_(kb1) + E_(gb1) = E_(kb2) + E_(gs2)$

$E_(kb1) + E_(gb1) = 0 + E_(gs2)$

$(1)/(2)*m*V_(b1) ^(2) + m*g*H_(b1) = m*g*H_(b2)$

$H_(b2) = (V_(b1) ^(2) )/(2g) + H_(b1)$

Replacing data:

$H_(b2) = (0.44^(2) )/(2*9.81) + 0.8$

$H_(b2) = (0.44^(2) )/(2*9.81) + 0.4$

HB2 ≈ 0.81 m

Related Questions

How many hours does earth take to complete one rotation?
Which is true about the radiation force of light shining on a surface? The force is greater if the light reflects back along its incident path than in some other direction. The force is greater if the light is absorbed instead of being reflected. The force is greater if the light is reflected in some direction other than back along the incident path.
A ball is thrown into the air with 100 J of kinetic energy, which is transformed to gravitational potential energy at the top of its trajectory.When it returns to its original level after encountering air resistance, its kinetic energy is __________.A) more than 100 J.B) Not enough information given.C) less than 100 J.D) 100 J.
The acrylic plastic rod is 20 mm long and 15 mm in diameter. If an axial load of 300 N is applied to it, determine the change in its length and the change in its diameter. Eₚ = 2.70 GPa, vₚ = 0.4.
As an object in motion becomes heavier, its kinetic energy _____. A. increases exponentially B. decreases exponentially C. increases proportionally D. decreases proportionally

What is the revolution ratio of two spur gears with one having 12 teeth and the other having 36 teeth

Answers

3:1 is the ratio i hope this belps

A small child weighs 60 N. If mommy left him sitting on top of the stairs, which are 12 m high, how much energy does the child have!Please help ASAP

Answers

Answer:

6000 joules

Explanation:

I jus learned dis

Answer:6000j

Explanation:

Hope that helps

G Water enters a house through a pipe 2.40 cm in diameter, at an absolute pressure of 4.10 atm. The pipe leading to the second-floor bathroom, 5.20 m above, is 1.20 cm in diameter. The flow speed at the inlet pipe is 4.75 m/s a) What is the algebraic expression for flow speed in the bathroom?
b) Calculate the flow speed in the bathroom.
c) What is algebraic expression for the pressure in the bathroom?
d) Calculate the water pressure in the bathroom. Report your answer in the (atm) unit.

Answers

Answer:

A) A₁ V₁ = A₂V₂

B) V₂ = 19 m /s

C) P₁ + (1/2)ρv₁² = P₂ + (1/2)ρv₂² + (h₂ - h₁ )ρg

D) P₂ = 1.88 atm

Explanation:

A) From the piaget's theory of conservation of volume, we can calculate the rate of flow of water from;

A₁ V₁ = A₂V₂

Where;

A₁ and A₂ are area of cross section V₁ and V₂ are velocity of flow at two places along pipe.

B) Using the formula given in A above, we obtain;

π x 1.2² x 4.75 = π x 0.6² x V₂

V₂ x 0.36 = 6.84

V₂ = 6.84/0.36

V₂ = 19 m /s

c ) To find pressure we shall apply Bernoulli's theorem in fluid dynamics;

P₁ + (1/2)ρv₁² = P₂ + (1/2)ρv₂² + (h₂ - h₁ )ρg

Where;

P₁ and P₂ are pressure at ground and second floor respectively

v₁ and v₂ are velocity at ground and second floor respectively

h₁ and h₂ are height at ground and second floor respectively ρ is density of water.

Thus, plugging in the relevant values to obtain;

4.1 x 10⁵ + (1/2 x 1000 x 4.75²) = P₂ + (1/2 x 1000 x 19²) + (5.2 x 1000 x 9.8)

(4.1 x 10⁵) + (0.11 x 10⁵) = P₂ + (1.8 X 10⁵) + (0.51 X 10

P₂ = 1.9 X 10⁵ N/m² = 1.88 atm

What does a planet need in order to retain an atmosphere? How does an atmosphere affect the surface of a planet and the ability of life to exist?

Answers

Answer:

Explained

Explanation:

In order to retain atmosphere a planet needs to have gravity. A gravity sufficient enough to create a dense atmosphere around it, so that it can retain heat coming from sun. Mars has shallow atmosphere as its gravity is only 40% of the Earth's gravity. Venus is somewhat similar to Earth but due to green house effect its temperature is very high. Atmosphere has a huge impact on the planets ability to sustain life. Presence of certain kind gases make the atmosphere poisnous for life. The atmosphere should be such that it allows water to remain in liquid form and maintain an optimum temperature suitable for life.

To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula y1(x,t)=Asin(kx−ωt)
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.
1. Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.
2. At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?
3. At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
4. Which one of the following statements about the wave described in the problem introduction is correct?
A. The wave is traveling in the +x direction.
B. The wave is traveling in the −x direction.
C. The wave is oscillating but not traveling.
D. The wave is traveling but not oscillating.
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.
A. Acos(kx−ωt)
B. Acos(kx+ωt)
C. Asin(kx−ωt)
D. Asin(kx+ωt)

Answers

The definition of standing wave and trigonometry allows to find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Traveling waves are periodic movements of the media that transport energy, but not matter, the expression to describe it is:

y₁ = A sin (kx -wt)

Where A is the amplitude of the wave k the wave vector, w the angular velocity and x the position and t the time.

1. Ask us to find the spatial and temporal part of the standing wave.

To form the standing wave, two waves must be added, the reflected wave is:

y₂ = A sin (kx + wt)

The sum of a waves

y = y₁ + y₂

y = A (sin kx-wt + sin kx + wt)

We develop the sine function and add.

Sin (a ± b) = sin a cos b ± sin b cos a

The result is:

y = 2A sin kx cos wt

They ask that the function be unitary therefore

The amplitude of each string

A_ {chord} = A_ {standing wave} / 2

The spatial part is

$y_e$ = A 'sin kx

The temporary part is:

$y_t$ = A ’cos wt

2. At position x = 0, what is the displacement of the string?

y = A ’cos wt

The string moves in an oscillating motion.

3. At what point the string is straight.

When the string is straight its displacement is zero x = 0, the position remains.

y = A ’cos wt

For the amplitude of the chord to be zero, the cosine function must be zero.

wt = (2n + 1) $(\pi)/(2)$

the first zero occurs for n = 0

wt = $(\pi )/(2)$

t = $(\pi )/(2w)$

4) The traveling wave described in the statement is traveling in the positive direction of the x axis, therefore the correct statement is:

A. The wave is traveling in the +x direction.

5) The wave traveling in the opposite direction is

y₂ = A sin (kx + wt)

The correct answer is:

D. Asin(kx+ωt)

In conclusion using the definition of standing wave and trigonometry we can find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Learn more about standing waves here: brainly.com/question/1121886

What is suedo force.

Answers

What is pseudo force?

A pseudo force, also called a fictitious force or an inertial force, is an apparent force that acts on all bodies whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.

Other Questions

The thickness of a $1 bill is 0.11 mm. If you have a stack of $1 bills 450 m tall, how much money do you have?

A certain x-ray tube requires a current of 7 mA at a voltage of 80 kV. The rate of energy dissipation is:

The main force(s) acting on the puck after receiving the kick is (are):_________.A) a downward force of gravity and an upward force exerted by the surfaceB) a downward force of gravity, and a horizontal force in the direction of motionC) a downward force of gravity, an upward force exerted by the surface, and a horizontal force in the direction of motionD) a downward force of gravityA) a downward force of gravity and an upward force exerted by the surface

A woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N. The board is supported at each end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the woman standing?