1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vovangra [49]
3 years ago
10

A 17.6-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally

on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 3.58 m/s in 1.77 s. In the process, the spring is stretched by 0.250 m. The block is then pulled at a constant speed of 3.58 m/s, during which time the spring is stretched by only 0.0544 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.

Physics
1 answer:
leonid [27]3 years ago
3 0

In order get the block up to a speed of 3.58 m/s in 1.77 s, it must undergo an acceleration <em>a</em> of

<em>a</em> = (3.58 m/s) / (1.77 s) ≈ 2.02 m/s²

When the spring is getting pulled, Newton's second law tells us

• the net vertical force is

∑ <em>F</em> = <em>n</em> - <em>mg</em> = 0

where ∑ <em>F</em> is the net force, <em>n</em> is the magnitude of the normal force, and <em>mg</em> is the weight of the block - it follows that <em>n</em> = <em>mg</em> ; and

• the net horizontal force is

∑ <em>F</em> = <em>F</em> - <em>f</em> = <em>ma</em>

where <em>F</em> is the applied force, <em>f</em> is kinetic friction, <em>m</em> is the block's mass, and <em>a</em> is the acceleration found earlier. <em>F</em> stretches the spring by <em>x</em> = 0.250 m, so we have

<em>F</em> - <em>f</em> = <em>kx</em> - <em>µn</em> = <em>kx</em> - <em>µmg</em> = <em>ma</em>

where <em>k</em> is the spring constant and <em>µ</em> is the coefficient of kinetic friction.

When the block is being pulled at a constant speed, Newton's second law says

• the net vertical force is still

∑ <em>F</em> = <em>n</em> - <em>mg</em> = 0

so that <em>n</em> = <em>mg</em> again; and

• the net horizontal force is

∑ <em>F</em> = <em>F</em> - <em>f</em> = 0

This time, <em>F</em> stretches the spring by <em>y</em> = 0.0544 m, so we have

<em>F</em> - <em>f</em> = <em>ky</em> - <em>µmg</em> = 0

Solve the equations in boldface for <em>k</em> and <em>µ</em> :

<em>kx</em> - <em>µmg</em> = <em>ma</em>

<em>ky</em> - <em>µmg</em> = 0

==>   <em>k</em> (<em>x</em> - <em>y</em>) = <em>ma</em>

==>   <em>k</em> = <em>ma</em> / (<em>x</em> - <em>y</em>)

==>   <em>k</em> = (17.6 kg) (2.02 m/s²) / (0.250 m - 0.0544 m) ≈ 182 N/m

Then

<em>ky</em> - <em>µmg</em> = 0

==>   <em>µ</em> = <em>ky </em>/ (<em>mg</em>)

==>   <em>µ</em> = (182 N/m) (0.0544 m) / ((17.6 kg) <em>g</em>) ≈ 0.0574

You might be interested in
Mercury was named after the roman god of speed why is it an appropriate name for the planet
elena-14-01-66 [18.8K]
Because it's the planet in our solar system with the shortest,
fastest orbit around the sun ... only 88 Earth days.

The people who named it didn't know that ... they still thought that
the sun and all the planets revolve around the Earth.  But they did
see it zip from one side of the sun to the other, faster than any other
planet ... the result of having the shortest, fastest orbit of any planet.
5 0
3 years ago
If you are sitting in the back seat of a car that makes a hard left turn, you will feel pushed toward the right side of the car.
Sonja [21]

Answer:

Inertia

Explanation:

Your body is naturally resisting turning left, as it wants to continue straight. So if feels like you are going right.

3 0
3 years ago
Read 2 more answers
Even though you are getting closer to the sun as you ascend into the toposphere, why does the temperature drop?
pishuonlain [190]

Answer: The lower areas of the Atmosphere have a high temperature through the heats from the ground.

Explanation: High temperature experienced on the Earth surface is majorly caused by heats from the ground ( Earth crust).As a person ascend up to the Toposphere the temperature continues to reduce because because the heat from the ground is reduced as the heights increased.

It has been proven that as a person ascends into the Toposphere the amount of air and pressure reduces this will eventually lead to expansion of the gas particles which will then reduce the temperature.

4 0
3 years ago
Read 2 more answers
6) The best way to reduce force in a car wreck when impulse stays the same is to
UkoKoshka [18]

Answer:

c. increase momentum

Explanation:

When cars bounce off each other, or rebound, there is a larger change in momentum and therefore a larger impulse. A larger impulse means that a greater force is experienced by the occupants of the cars. When cars crumple together, there is a smaller change in momentum and therefore a smaller impulse.

3 0
2 years ago
Usually, tall trees collapse in stroms?<br>​
sergey [27]
Taller trees are more likely to fall during storms than short trees.
3 0
3 years ago
Read 2 more answers
Other questions:
  • As you increase the number of supporting strings, what happens to the force needed to lift the bottom block
    11·1 answer
  • What is the value of x in the expression: x = p(p+q) + 4 if p = -2 and q = 7
    7·1 answer
  • At Alpha Centauri's surface, the gravitational force between Alpha Centauri and a 2 kg mass of hot gas has a magnitude of 618.2
    6·2 answers
  • A light bulb radiates 110 nW of single-frequency sinusoidal electromagnetic waves uniformly in all directions. Calculate the ave
    5·1 answer
  • A frog leaps vertically into the air and encounters no appreciable air resistance.
    7·1 answer
  • What happens to the pwc when the throttle is released?
    15·1 answer
  • A system releases 680 kj of heat and does 150 kj of work on the surroundings.what is the change in internal energy of the system
    9·1 answer
  • Which liquid is the most viscous?<br><br> syrup<br> water<br> milk<br> apple juice
    8·2 answers
  • Do you think scientists will ever be able to recreate a living creature from the distant past successfully?
    8·2 answers
  • Pylon cables in the National Grid have some resistance. Power (watts) = Current2 (amperes) x Resistance (ohms) Looking at the po
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!