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
50 points: can someone help me with this question please: A classroom is 5.345m long, 4.128m wide, and 3.859m high. What is the
lesya [120]

this is basically the same as volume, no?

So, 5.345*4.128*3.859=85.145

5 0
3 years ago
Read 2 more answers
Why are all bodies in nature electrically neutral? short answer please​
DENIUS [597]

Answer: because they have equal numbers of protons

Explanation: Atoms are electrically neutral because they have equal numbers of protons (positively charged) and electrons (negatively charged). If an atom gains or loses one or more electrons, it becomes an ion

3 0
2 years ago
What is the temperature increase of 4.0 kg of water when heated by an 800-W immersion heater for 10 min? (cw = 4 186 J/kg⋅°C)
Llana [10]

Answer:

option C

Explanation:

given,

mass of water = 4 Kg

Water is heated to = 800 W

time of immersion = 10 min

                              = 10 x 60 = 600 s

using equation of specific heat  

Q = m S ΔT

S is the specific heat capacity of water which is equal to 4182 J/kg°C.

and another formula of heat

Q = Pt

now,

P t =  m S ΔT

800 x 600  = 4 x 4182 x ΔT

ΔT = 29° C

temperature increased is equal to ΔT = 29° C

Hence, the correct answer is option C

3 0
3 years ago
g Where is the dielectric constant and A is the area of the capacitor plates. The charge q and voltage Vc across the capacitor p
aev [14]

Answer:

<u>Capacitor and the dielectrics:</u>

"The capacitor is a charge,q storing device as it is subjected to the potential difference between the different plates and thus results in the difference of charge decomposition between the two plates."

<u>Formula:</u>C= ∈°(A/d),

<u>Unit:</u>  Farad,F.

  • <u>Purpose of the Dielectrics:</u>

In order to store or hold the optimum number of charge particles,q between the plates we have a number of insulators which are used as the medium between the two plates.While, it separates both the plates from one another.

Explanation:

<u>Dielectric Constants in the capacitors:</u>

In order to hold the number of charges in between the plates of the capacitor a specific medium or substrate is placed(mostly the insulators). As it covers the area between the two capacitors, while it can decrease and increase by the action of the movable plate of the capacitor.

Now, it increase the capcitative power of the capacitor by decreasing the potential difference between the two plates, along with which the electromagnetic field is also greatly reduced.As the interaction between the two plates is greatly reduced, as they are covered and well protected by the sheet or membrane of insulting medium around them.

6 0
3 years ago
Blank occurs when salt is evenly mixed with water
podryga [215]
I think solution because it dissolves
6 0
3 years ago
Other questions:
  • The distance between stars is typically measured in
    15·2 answers
  • Which of these accurately describes the products of a reaction?
    14·2 answers
  • The frequency of a given region of the electromagnetic spectrum ranges from 3 × 1016 − 3 × 1019 hertz. Which type of wave is fou
    13·1 answer
  • what is required to bring about a phase change 1.an increase or decrease in pressure 2.an increase or decrease in energy 3.an in
    10·2 answers
  • Which are examples of projectile motion?
    13·1 answer
  • What is the area of a rectangle whose sides are 3.2 m and 8.01 m? Answer in units of m²
    8·2 answers
  • A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction.Part AIf at a particular instant and at a certa
    14·1 answer
  • The caste system is an example of​
    5·1 answer
  • It is rate for any motion to
    7·1 answer
  • The speed of sound in water is 1,492 m/s. A sonar signal is sent straight down from a ship at a point just below the water's sur
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!