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Kisachek [45]
3 years ago
13

A block of weight mg sits on an inclined plane as shown in (Figure 1) . A force of magnitude F1 is applied to pull the block up

the incline at constant speed. The coefficient of kinetic friction between the plane and the block is μ.What is the total work WfricWfricW_fric done on the block by the force of friction as the block moves a distance LLL up the incline? Express the work done by friction in terms of any or all of the variables μμmu, mmm, ggg, θθtheta, LLL, and F1F1F_1.
Physics
1 answer:
svlad2 [7]3 years ago
4 0

Answer:

W = (F1 - mg sin θ) L,   W = -μ  mg cos θ L

Explanation:

Let's use Newton's second law to find the friction force. In these problems the x axis is taken parallel to the plane and the y axis perpendicular to the plane

Y Axis  

       N - W_{y} =

       N = W_{y}

X axis

       F1 - fr - Wₓ = 0

       fr = F1 - Wₓ

Let's use trigonometry to find the components of the weight

     sin θ = Wₓ / W

     cos θ = W_{y} / W

      Wₓ = W sin θ

      W_{y} = W cos θ

We substitute

      fr = F1 - W sin θ

Work is defined by

        W = F .dx

        W = F dx cos θ

The friction force is parallel to the plane in the negative direction and the displacement is positive along the plane, so the Angle is 180º and the cos θ= -1

         

        W = -fr x

        W = (F1 - mg sin θ) L

Another way to calculate is

         fr = μ N

         fr = μ W cos θ

the work is

         W = -μ  mg cos θ L

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A 1. 30 kg block slides with a speed of 0. 855 m/s on a frictionless horizontal surface until it encounters a spring with a forc
boyakko [2]

a) For 0 compressions:

potential energy = U =  0 J

kinetic energy = k = 0.383 J

total mechanical energy = E = 0.383 J

b) For compression of 1 cm:

potential energy = U = 0.0228 J

kinetic energy = k = 0.155 J

total mechanical energy = E = 0.383 J

c) For compression of 2 cm :

potential energy = U = 0.1104 J

kinetic energy = k = 0.272 J

total mechanical energy = E = 0.383 J

d) For compression of 3cm:

potential energy  = U = 0.248 J

kinetic energy = k = 0.177 J

total mechanical energy = E = 0.383 J

<h3>Method for solving:</h3>

The equations for kinetic energy is:

k= 1/2*m*v^{2}

The equation for elastic potential energy is:

U= 1/2*ks*x^{2}

Where,

m= mass of the block

v= velocity

ks= spring constant

x= displacement of the spring

(a)when compression= 0 cm

U= 1/2*ks*v{2}

U= 1/2*552*(0)^{2}

 = 0 J

Kinetic energy:

k= 1/2*m*x^{2}

k= 1/2*(1.05)*(0.855)^{2}

k= 0.383 J

Mechanical energy:

E= k + U

E= 0.383+0

E= 0.383 J

There will be no work done by friction or any other dissipative force, hence this energy will be conserved, or it will remain constant (like air resistance). This indicates that only spring potential energy will be created from the kinetic energy (there is no thermal energy due to friction, for example).

(b) spring potential = ?

U= 1/2* 457 N/m*(0.01)^{2}

U= 0.0228 J

Since the mechanical energy must remain constant, we may calculate the kinetic energy using the mechanical energy equation:

E= k + U

0.383= k + 0.0228

k= 0.383 - 0.228

k= 0.155

(c)spring constant when x= 0.02

U= 1/2*552*(0.02)^{2}

U= 0.1104 J

Using the equation of mechanical energy:

E= k +U

0.383= k+ 0.1104

k= 0.383 - 0.1104

k= 0.272 J

(d) U= 1/2*552*(0.03)^{2}

U= 0.2484 J

E= 0.383 J

k = E - U

k= 0.383- 0.206

k= 0.177

To learn more about spring potential energy visit:

brainly.com/question/28168175

#SPJ4

3 0
2 years ago
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