A 1.10-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e).

The right end of a horizontal spring labeled k is attached to a wall. Five images show five configurations as a block labeled m approaches, compresses, and then moves away from the spring.
In figure a, the block is to the left of the spring, and an arrow above the block points to the right.
In figure b, the block is just touching the uncompressed spring, and an arrow labeled vector vi above the block points to the right.
In figure c, the block has compressed the spring by a distance d, and a label indicates vector vf = 0.
In figure d, the block is just touching the uncompressed spring, and an arrow labeled vector v above the block points to the left.
In figure e, the block is a distance D away from the spring, and a label indicates vector v = 0.
(a)
Find the distance of compression d (in m).
m
(b)
Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d).
m/s
(c)
Find the distance D (in m) where the object comes to rest.
m
(d)
What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving to the left?
m

Answer:

(a) Approximately [tex]0.335\; \rm m[/tex].

(b) Approximately [tex]1.86\; \rm m\cdot s^{-1}[/tex].

(c) Approximately [tex]0.707\; \rm m[/tex].

(d) Approximately [tex]0.228\; \rm m[/tex].

Explanation:

Consider the conversion of energy in this object-spring system.

First diagram: Right before the object came into contact with the spring, the object carries kinetic energy [tex]\displaystyle \frac{1}{2}\, m \cdot {v_{i}}^2[/tex].

Second diagram: As the object moves towards the position in the third diagram, the spring gains elastic potential energy. At the same time, the object loses energy due to friction.

Third diagram: After the velocity of the object becomes zero, it has moved a distance of [tex]D[/tex] and compressed the spring by the same distance.

The sum of these two energies should match the initial kinetic energy of the object (before it comes into contact with the spring.) That is:

[tex]\displaystyle \frac{1}{2}\, m \cdot {v_{i}}^{2} = (\mu\cdot m \cdot g) \cdot D + \frac{1}{2}\, k \cdot D^2[/tex].

Assume that [tex]g = 9.81\; \rm m \cdot s^{-2}[/tex]. In the equation above, all symbols other than [tex]D[/tex] have known values:

Substitute in the known values to obtain an equation for [tex]D[/tex] (where the unit of [tex]D\![/tex] is [tex]m[/tex].)

[tex]3.178 = 2.69775\, D + 25\, D^2[/tex].

[tex]2.69775\, D + 25\, D^2 + 3.178 = 0[/tex].

Simplify and solve for [tex]D[/tex]. Note that [tex]D > 0[/tex] because the energy lost to friction should be greater than zero.

[tex]D \approx 0.335\; \rm m[/tex].

The energy of the object-spring system in the third diagram is the same as the elastic potential energy of the spring:

[tex]\displaystyle \frac{1}{2}\,k\, D^2 \approx 2.81\; \rm J[/tex].

As the object moves to the left, part of that energy will be lost to friction:

[tex](\mu \cdot m \cdot g) \, D \approx 0.905\; \rm J[/tex].

The rest will become the kinetic energy of that block by the time the block reaches the position in the fourth diagram:

[tex]2.81\; \rm J - 0.905\; \rm J \approx 1.91\; \rm J[/tex].

Calculate the velocity corresponding to that kinetic energy:

[tex]\displaystyle v =\sqrt{\frac{2\, (\text{Kinetic Energy})}{m}} \approx 1.86\; \rm m \cdot s^{-1}[/tex].

As the object moves from the position in the fourth diagram to the position in the fifth, all its kinetic energy ([tex]1.91\; \rm J[/tex]) would be lost to friction.

How far would the object need to move on the surface to lose that much energy to friction? Again, the size of the friction force is [tex]\mu \cdot m \cdot g[/tex].

[tex]\displaystyle (\text{Distance Travelled}) = \frac{\text{(Work Done by friction)}}{\text{(Size of the Friction Force)}} \approx0.707\; \rm m[/tex].

Similar to (a), solving (d) involves another quadratic equation about [tex]D[/tex].

Left-hand side of the equation: kinetic energy of the object (as in the fourth diagram,) [tex]1.91\; \rm J[/tex].

Right-hand side of the equation: energy lost to friction, plus the gain in the elastic potential energy of the spring.

[tex]\displaystyle {1.91\; \rm J} \approx (\mu\cdot m \cdot g) \cdot D + \frac{1}{2}\, k \cdot D^2[/tex].

[tex]25\, D^2 + 2.69775\, D - 1.90811\approx 0[/tex].

Again, [tex]D > 0[/tex] because the energy lost to friction is greater than zero.

[tex]D \approx 0.228\; \rm m[/tex].

The energy transferred between the object and the spring as a closed system, therefore, conserved are;

(a) The distance of compression, d ≈ 0.3354 meters

(b) The speed in the un-stretched position wen the object is sliding to the left, v ≈ 1.8623 m/s

(c) The distance where the object comes to rest, D ≈ 0.7071 m

(d) The distance the object will come to rest attached to the spring, D ≈ 0.2278 m

The reason the above values are correct are as follows;

The known parameters are;

Mass of the object, m₁ = 1.10 kg

Coefficient of friction, μ = 0.250

The initial speed of the object, [tex]v_i[/tex] = 2.60 m/s

Force constant of the spring, K = 50.0 N/m

Distance the spring is compressed by the object = d

(a) Conservation of energy principle

[tex]Kinetic \ energy = \dfrac{1}{2} \cdot m\cdot v^2[/tex]

Work done = Force × Distance

Friction force, [tex]F_f[/tex] = W × μ

Weight, W = m·g

Weight = Mass × Acceleration

Energy transferred by object = Work done by spring + Work done by friction

[tex]Energy \ transferred \ by \ object = Kinetic \ energy = \dfrac{1}{2} \times 1.10\times 2.60^2 = 3.718[/tex]

Energy transferred by object = 3.718 J

[tex]Work \ done \ by \ spring = \dfrac{1}{2} \cdot k\cdot x^2[/tex]

[tex]Work \ by \ spring \ to \ bring \ object \ to \ rest, \ W_{spring} = \dfrac{1}{2} \times 50\times d^2[/tex]

[tex]W_{spring}[/tex] = 25·d²

Work done by friction, [tex]W_{friction}[/tex] = 1.10×9.81×0.250×d = 2.69775·d

Therefore;

3.718 = 25·d² + 2.69775·d

25·d² + 2.69775·d - 3.718 = 0

Solving gives

The distance of the compression d ≈ 0.3354 m

(b) The energy given by the spring = 25·d²

The work done by friction, [tex]W_{friction}[/tex] = 2.69775·d

Kinetic energy given to object = 0.55·v²

0.55·v² = 25·d² - 2.69775·d

0.55·v² = 25×0.3354² - 2.69775×0.3354

∴ v = √(3.4682) = 1.8623

The velocity of the object at the un stretched position, v ≈ 1.8623 m/s

(c) The kinetic energy, K.E. of the object on the way left is given as follows;

K.E. = 0.5 × 1.10 kg × 3.4682 m²/s² = 1.90751 J

The work done by friction before object comes to rest = 2.69775·D

[tex]D = \dfrac{1.90751 \, J}{2.69775 \, N} \approx 0.7071 \, m[/tex]

The distance where the object comes to rest, D ≈ 0.7071 m

(d) The work done on spring, [tex]W_{spring}[/tex] = 25·D'²

Work done on friction, [tex]W_{friction}[/tex] = 2.69775·D'

Kinetic energy of object, K.E. ≈ 1.90751 J

K.E. = [tex]W_{spring}[/tex] + [tex]W_{friction}[/tex]

1.90751 ≈ 25·D'² + 2.6775·D'

25·D'² + 2.6775·D' - 1.90751 = 0

Solving with a graphing calculator gives;

D' ≈ 0.2278 m

The new value of the distance D = 0.2278 m

Learn more about the energy conservation principle here:

https://brainly.com/question/928985

Question 11 of 15
When hydrogen is attached to the more highly electronegative oxygen atom in
a water molecule,
A. the electronegative atom becomes strongly positive
B. the hydrogen atom becomes partially positive
O C. the oxygen atom becomes partially negative

If answer is right WILL GIVE BRAINLIEST
D. the hydrogen atom becomes partially negative

Suppose a rocket-propelled motorcycle is fi red from rest horizontally across a canyon 1.00 km wide. (a) What minimum constant acceleration in the x-direction must be provided by the engines so the cycle crosses safely if the opposite side is 0.750 km lower than the starting point? (b) At what speed does the motorcycle land if it maintains this constant horizontal component of acceleration? Neglect air drag, but remember that gravity is still acting in the negative y-direction.

PLZ HELP!!!!!!! ILL GIVE U BRAINLIEST

What statements accurately describe sunspots? Check all that apply.
Sunspots are storms on the Sun's surface.
Sunspots are marked by intense magnetic activity.
Sunspots produce solar flares and hot gassy ejections.
Sunspots can affect Earth's climate.
Sunspots are cool areas where the Sun is covered by clouds.

PLEASE HELP 50 POINTS!!!!!!!!!!!!!!!

Andrew and Deshawn are teammates on a high school soccer team. They’ve been playing soccer together for years. They both play the center forward position. Some years, Andrew is better than Deshawn and serves as the team’s starter. Other years, Deshawn is the stronger player and gets the most playing time. They are both very competitive with each other. Although they know each other well, they have never been friends.

In practice yesterday, the team was running drills in the rain. Deshawn slipped in the mud and collided with Andrew. Andrew hurt his knee badly in the fall and will have to sit out for several weeks.

The next day, Andrew told everyone at school that Deshawn hurt him on purpose to get more playing time. Deshawn retaliated by sharing private information about Andrew on social media. Andrew’s best friend Mateo saw the collision. He knows it was a complete accident.

Pick the role of Andrew, Deshawn, or Mateo.
What are the main issues/problems from this person’s perspective?
What ethical issues are involved for this person?
Why are these ethical issues relevant for this person?
How should the person you chose handle the situation?

Hellllllpppppp what happens

The path of a projectile fired at an angle above the horizontal is best described as

What is velocity in science

I am so close to wanting to drop out of physics


I'm in college and idk why physics has to be this tough. I took physics back in high school, and it was super easy & I had a really nice teacher.


But now that I'm in college, my professor does no help and literally 60 people dropped out of his class bc his class is hard. I am going to fail my midterm this week. idk what to do and Im sick and tired but its a requirement.

I literally wanna drop out of college bc of physics

1.What is the mass of an object that weighs 98 N?​

Your car is initially at rest when your hit that gas and the car begins to accelerate at a rate of 2.857 m/s/s. The acceleration lasts for 15.5 s. What is the final speed of the car and how much ground does it cover during this acceleration?

What President is responsible for eliminating most vending machines from the cafeterias of public schools ?

Which best describes a difference between laser light and regular light?
Laser light is less concentrated.
Laser light has a beam that spreads out.
O Laser light is made of one specific color.
O Laser light pumps out light particles one at a time.

1)
You travel east at 50 km/hr and then north at 75 km/hr. What is your Resultant Velocity in km/h?
(Remember the angle) (5pts)

Which Statement describes Newton's law of universal gravitation?

Mass has little effect on gravity between objects

gravity pushes objects away from Earth's center

gravity does not act between Earth and Moon

every object in the universe attracts every other objects

>You will get 100 points for answering this!

The Plateau of Tibet is a dry place. Do you think the wide-leafed plant fossils found on the plateau could grow there today? Explain your answer.

Which of the following is not a part of the appendicular skeleton
a. femur
b. scapula
c.phalanges
d.hyoid

Which landform represents a piece of land that is formed when a river splits before flowing into the ocean?

Delta
Glacier
Lake
Mountain

Question 3 of 10
A 0.057 kg tennis ball and a tennis racket collide. The racket has an initial
momentum of -1.75 kg-m/s and a final momentum of -1.25 kg-m/s. The ball
has an initial momentum of 0.00684 kg-m/s. If you assume the collision is
elastic, what is the final velocity of the ball?
A. -0.50 m/s
B. -52.48 m/s
C. -2.99 m/s
d
D. -8.65 m/s

A power cycle operating between hot and cold reservoirs at 500 K and 300 K, respectively, receives 1000 kJ by heat transfer from the hot reservoir. The magnitude of the energy discharged by heat transfer to the cold reservoir must satisfy

Two wires A and B made of the same material and having the same lengths are connected across the same voltage source. If the power supplied to wire A is six times the power supplied to wire B, what is the ratio of their diameters

50 POINTS PLSS
Your car is initially at rest when your hit that gas and the car begins to accelerate at a rate of 2.857 m/s/s. The acceleration lasts for 15.5 s. What is the final speed of the car and how much ground does it cover during this acceleration?

Sand is made of tiny pieces of rock that have been worn
down by wind and water. Explain why the formation of
sand is a physical change.

explain why a wrecking ball can destroy a building, but a yo-yo cant. Use the term kinetic energy in your explanation.

show answer No Attempt 50% Part (b) Calculate the non-relativistic speed of these electrons v in m/s.

Your are part of a team to help design the atrium of a new building.Your boss, the manager of the project, wants to suspend a 6.2 kg sculpture high over the room by hanging it from the ceiling using thin, clear fishing line (string) so that it will be difficult to see how the sculpture is held up. The only place to fasten the fishing line is to a wooden beam which runs around the edge of the room at the ceiling.The fishing line that she wants to use will hold 10 kg so she suggests attaching two lines to the sculpture to be safe. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has the first line making an angle of 12.67∘with the ceiling and the second line making an angle of 16.15∘ with the ceiling. She knows you took physics, so she asks you if her design can work.
How much force would the first line exert on the beam holding it up?
Assume that g=9.8 m/s−2.

A yo-yo is attached to the end of a string. A professional yo yo is spinning it by the string around in a circular
motion. All of a sudden he lets go of the string. What direction is the yo yo moving in initially?

A stone is thrown vertically upward with the velocity of 25 m/s. How long day
it take to reach the maximum height? Also calculate the height​

The cheetah, the fastest land animal, can sprint at 30 m/s. Could the cheetah get a speeding
ticket on a highway where the speed limit is 55 mph?

4. A 65 kg woman is inside an elevator. Calculate her apparent weight (Normal Force) for the following cases:

a. The elevator moves at constant speed of 10 m/s downward (2 pts)
b. The elevator accelerates upward at a constant rate of 2.4 m/s2 (2 pts)
c. If the scale read 450 N. Find the magnitude and direction of the elevator’s acceleration. (3 pts)