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
KATRIN_1 [288]
3 years ago
7

A 4.5 kg box slides down a 4.3-m-high frictionless hill, starting from rest, across a 2.0-m-wide horizontal surface, then hits a

horizontal spring with spring constant 510 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.0-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.22. What is the speed of the box just before reaching the rough surface? What is the speed of the box just before hitting the spring? How far is the spring compressed? Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?
Physics
1 answer:
Rainbow [258]3 years ago
8 0

Answer:

speed  before reaching rough surface = 9.18 m/s

speed before hitting spring = 8.70 m/s

spring compression = 82 cm

number of complete trip = 9

Explanation:

Lets say

Position 1: On top of hill

Position 2: down the hill

Position 3: after the rough surface

Position 4: after hitting the spring

We'll strictly use conservation of energy for this equation

Potential energy on top of energy is full converted into kinetic energy down the hill (since surface is frictionless)

Hence, PEg1 = KE2

mgh = (1/2)mv2^2

(4.5)(9.8)(4.3) = (1/2)(4.5)v2^2

189.63 = (1/2)(4.5)v2^2

v2^2 = 2(9.8)(4.3) = 84.28

v2 = sqrt(84.28) = 9.18 m/s

After down the hill, it passes a rough surface. So some of the energy is loss due to friction forces

Friction force, Ff = u (coeff of kinetic friction ) x N (normal force)

Normal force, N = weight of box = mg = 4.5 x 9.8

Ff = 0.22 x 4.5 x 9.8

Work done / Energy loss = Wf = Ff x d (distance)

Wf = 0.22 x 4.5 x 9.8 x 2 = 19.404

Energy after passing the rough surface is totally kinetic energy

KE3 = KE2 - Wf = 189.63 - 19.404 = 170.226

speed after rough surface,

(1/2)mv3^2 = 170.226

v3 = sqrt((2 x 170.226)/4.5) = 8.70 m/s

After hitting the spring, all the kinetic energy is converted into potential energy of spring

170.226 = (1/2)kx^2

x^2 = 2 x 170.226 / 510     {note that constant of spring, k = 510}

x^2 = 0.668

x = sqrt(0.668) = 0.82m (82 cm)

To calculate complete trip before the box coming to rest, note that the only place where it loss energy is at the rough surface.

Energy before the first time pass rough surface = 189.63

Energy loss each time passing rough surface = 19.404

189.63 / 19.404 = 9.773 (9 complete with balance of 0.773)

That mean, the box will pass the rough surface 9 complete trip before coming to rest

You might be interested in
Which letter represents the wavelength of the wave?<br><br>A: a<br><br>B: b<br><br>C: c<br><br>D: d​
KATRIN_1 [288]

Answer:

D

Explanation:

Shows the distance between each new wave.

4 0
3 years ago
Read 2 more answers
Một dây dẫn mảnh được uốn thành một cung tròn bán kính 10cm, góc ở tâm bằng 1200, đặt trong không khí. Trong dây dẫn có dòng điệ
olga2289 [7]

Answer:

Diana and that

Explanation:

muyayyano

7 0
2 years ago
how would your weight change with time if you were on s space ship traveling away from Earth toward the moon
astra-53 [7]

Well, before we discuss that, I think we have to carefully understand
and agree on something.  We have to be very clear about what we
mean by 'weight' ...  is it what you feel, or is it the product of

           (your mass) x (the acceleration of gravity where you are).

If you're on a space ship, then any time your engine is not burning,
you feel weightless.  It doesn't matter where you are, or what body
you may be near.  If you're not doing a burn, and the only force on
you is the force of gravity, then you don't feel any weight at all.

But of we say that your 'weight' is the product of

           (your mass) times (the acceleration of gravity where you are),

then it depends on where you are, and whether you're close to
the Earth or closer to the moon.  You may not feel it, but you're
going to have weight, and it's going to change during your trip
in space.

You know that the force of gravity depends on how far you are
from the body that's attracting you.

-- As you travel from the Earth to the moon, gravity will pull you
less and less toward Earth, and more and more toward the moon. 

-- Your weight will get less and less, until you reach the point
in space where the gravitational attractions are equal in both
directions.  That's about 24,000 miles before you reach the
moon ... about 90% of the way there.  At that point, your weight
is really zero, because the pull toward the Earth and the pull toward
the moon are equal.

-- From there, the rest of the way to the moon, your weight will
start to grow again.  It begins at zero at the 'magic point', and it
grows and grows until you reach the moon's surface.  When
you're there, your weight has grown to about 1/6 of what you
weigh on Earth, and it won't get any bigger.  If you weigh
120 pounds on Earth, then you weigh about 19.86 pounds on
the moon ... PLUS your space suit, boots, heater/air conditioner,
oxygen tank, radiation shielding, radio, and all the other stuff that
you need to survive on the moon for a few hours.
8 0
2 years ago
I will give brainlisted for the correct answer!
Levart [38]
There are no measurements to work with. you'll need to measure the indicated lines with a ruler (most likely in cm) in order to obtain data to use!
3 0
2 years ago
3. A stone is thrown vertically upwards from the top of a building 50 m tall with an initial
san4es73 [151]

Answer:

13.4436

Explanation:

8 0
3 years ago
Other questions:
  • Which of the following types of weather data is collected in inches or centimeters?
    15·2 answers
  • When measuring the speed of a snail, a good unit to use is millimeters per minute. A snail takes 12 hours to travel 5 meters. Wh
    9·1 answer
  • What wave have a frequency of less then 20hz
    10·1 answer
  • Can someone help me on question 1?
    14·1 answer
  • What is v^2=0.05-4.9 please i need this asap​
    11·1 answer
  • Wave 1 carries more energy than Wave 2. Wave 3 carries more energy than Wave 2. Keeping speed constant, the greatest amount of e
    7·1 answer
  • A car has momentum, p=10880 kg m/s, east. If the car is traveling east at 16 m/s, its mass must be [m] kg.
    14·2 answers
  • Sometimes a person cannot clearly see objects close up or far away. To correct this type of vision, bifocals are often used. The
    5·1 answer
  • A wheel initially rotating at 12 rad/s decelerates uniformly to rest in 0.4 s. If the wheel has a rotational inertia of 0.5 kg.m
    15·1 answer
  • Which gives the work done by a torque during angular displacement?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!