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sattari [20]
4 years ago
8

A box of mass m slides down an inclined plane that makes an angle of φ with the horizontal. if the coefficient of kinetic fricti

on is μk, find an expression for the acceleration of the box down the slope. the acceleration due to gravity is g.
Physics
1 answer:
Schach [20]4 years ago
7 0
In a force diagram set-up, we name the angle of inclination theta, g as the acceleration due to gravity. In this case, the forces acting on the box going down is the weight itself impeded by the friction between the box and the inclined plane.

The weight of the box is expressed as mg sin theta
The frictional force is expressed as the normal force times the coefficient of friction that is expressed as mu g cos theta.

By Newton's second law of motion,  F = ma = mg sin theta - mu g cos theta
Thus, a = g (sin theta - u cos theta

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Consider two massless springs connected in parallel. Springs 1 and 2 have spring constants k1 and k2 and are connected via a thi
77julia77 [94]

Answer:

k1 + k2

Explanation:

Spring 1 has spring constant k1

Spring 2 has spring constant k2

After being applied by the same force, it is clearly mentioned that spring are extended by the same amount i.e. extension of spring 1 is equal to extension of spring 2.

x1 = x2

Since the force exerted to each spring might be different, let's assume F1 for spring 1 and F2 for spring 2. Hence the equations of spring constant for both springs are

k1 = F1/x -> F1 =k1*x

k2 = F2/x -> F2 =k2*x

While F = F1 + F2

Substitute equation of F1 and F2 into the equation of sum of forces

F = F1 + F2

F = k1*x + k2*x

= x(k1 + k2)

Note that this is applicable because both spring have the same extension of x (I repeat, EXTENTION, not length of the spring)

Considering the general equation of spring forces (Hooke's Law) F = kx,

The effective spring constant for the system is k1 + k2

3 0
3 years ago
Which type of energy is stored in chemical compounds and released in chemical reactions?
astraxan [27]

Answer:

potential

Explanation:

4 0
3 years ago
The track of a roller coaster is shown below. At which point will the riders experience centripetal acceleration?
valentinak56 [21]

Centripetal acceleration is applied in circular motion. Y is the point on the track that most closely resembles a circular path for the roller coaster.

4 0
3 years ago
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A long copper rod of diameter 2.0 cm is initially at a uniform temperature of 100°C. It is now exposed to an air stream at 20°C
Lisa [10]

Answer:

t = 4.0 min

Explanation:

given data:

diameter of rod = 2 cm

T_1 = 100 degree celcius

Air stream temperature =  20 degree celcius

heat transfer coefficient = 200 W/m2. K

WE KNOW THAT

copper thermal conductivity = k = 401 W/m °C

copper specific heat Cp = 385 J/kg.°C

density of copper = 8933 kg/m3

charateristic length is given as Lc

Lc = \frac{V}{A_s}

Lc = \frac{\frac{\pi D^2}{4} L}{\pi DL}

Lc = \frac{D}{4}

Lc = \frac{0.02}{6} = 0.005 m

Biot number is given as Bi = \frac{hLc}{k}

Bi = \frac{200*0.005}{401}

Bi = 0.0025

As Bi is greater than 0.1 therefore lumped system analysis is applicable

so we have

\frac{T(t) - T_∞}{Ti - T_∞} = e^{-bt} ............1

where b is given as

b = \frac{ hA}{\rho Cp V}

b = \frac{ h}{\rho Cp Lc}

b = \frac{200}{8933*385*0.005}

b = 0.01163 s^{-1}

putting value in equation 1

\frac{25-20}{100-20} = e^{-0.01163t}

solving for t we get

t = 4.0 min

6 0
3 years ago
The electric field in a certain region of Earth’s atmo- sphere is directed vertically down. At an altitude of 300 m the field ha
I am Lyosha [343]

Answer:

Net charge contained in the cubeq= 3.536×10^-6C

Explanation:

Formular for total flux in a cube is given as:

Total flux= E300Acos(180) + E200Acos(0)

Where A is crossectional area

Total flux= A(E200-E300)

Total flux= q/Eo

q= Eo×total flux

q=(8.84×10^-12)×(100)^2×(100-60)

q= 3.536×10^-6C

6 0
4 years ago
Read 2 more answers
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