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anyanavicka [17]
3 years ago
14

Two workers are sliding 350 kgkg crate across the floor. One worker pushes forward on the crate with a force of 390 NN while the

other pulls in the same direction with a force of 220 NN using a rope connected to the crate. Both forces are horizontal, and the crate slides with a constant speed. What is the crate's coefficient of kinetic friction on the floor
Physics
1 answer:
svetoff [14.1K]3 years ago
6 0

Answer:

\mu_k=0.18

Explanation:

First, we write the equations of motion for each axis. Since the crate is sliding with constant speed, its acceleration is zero. Then, we have:

x: T+F-f_k=0\\\\y:N-mg=0

Where T is the tension in the rope, F is the force exerted by the first worker, f_k is the frictional force, N is the normal force and mg is the weight of the crate.

Since f_k=\mu_k N and N=mg, we can rewrite the first equation as:

T+F-\mu_k mg=0

Now, we solve for \mu_k and calculate it:

\mu_k=\frac{T+F}{mg}\\ \\\mu_k =\frac{220N+390N}{(350kg)(9.8m/s^{2})} =0.18

This means that the crate's coefficient of kinetic friction on the floor is 0.18.

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blagie [28]

Answer:

W = 0.63 KJ

Explanation:

Work (W) is defined as the point product of force (F) by the distance (d)the body travels due to this force.  

W= F*d *cosα Formula (1)  

F : force (N)

d : displacement (m)

α : angle between force and displacement

Newton's second law:

∑F = m*a Formula (2)  

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the cart on the ramp and the y-axis in the direction perpendicular to it.

Forces acting on the cart

W: Weight of the cart : In vertical direction

FN : Normal force : perpendicular to the floor

f : Friction force: parallel to the floor

T : tension Force,  inclined at  θ=24.7° above the horizontal

Calculated of the W

W= m*g

W= 9.13 kg* 9.8 m/s² = 89.47 N

x-y components o the  tension force (T)

Tx = Tcosθ = T*cos 24.7° (N)

Ty = Tsin θ = T*sin 24.7°  (N)

Calculated of the FN  

We apply the formula (2)  

∑Fy = m*ay ay = 0  

FN +Ty- W = 0  

FN = W-Ty  

FN =  89.47-T*sin 24.7°

Calculated of the friction force (f)

f = μk*FN

f =(0.597)*(  89.47-T*sin 24.7° )

f= 53.41-0.249T

Calculated of the tension force of the rope (f)

We apply the formula (2) :

∑Fx = m*ax  ,  ax= 0 ,because the speed of the cart  is constant

Tx - f = 0

T*cos 24.7°-( 53.41 - 0.249T )= 0

T*cos 24.7° + 0.249T = 53.41

(1.1575)T = 53.41

T= (53.41) / (1.1575)

T= 46.14 N

Work done on the cart by the rope

We apply the formula (1)

W=T*d *cosα

W= (46.14 N)*(15.1 m) *(cos24.7)

W = 632.97 (N*m) = 632.97 (J)

W = 0.63 KJ

6 0
4 years ago
Light is incident along the normal to face AB of a glass prism of refractive index 1.54. Find αmax, the largest value the angle
marusya05 [52]

To solve this problem it is necessary to use the concepts related to Snell's law.

Snell's law establishes that reflection is subject to

n_1sin\theta_1 = n_2sin\theta_2

Where,

\theta = Angle between the normal surface at the point of contact

n = Indices of refraction for corresponding media

The total internal reflection would then be given by

n_1 sin\theta_1 = n_2sin\theta_2

(1.54) sin\theta_1 = (1.33)sin(90)

sin\theta_1 = \frac{1.33}{1.54}

\theta = sin^{-1}(\frac{1.33}{1.54})

\theta = 59.72\°

Therefore the \alpha_{max} would be equal to

\alpha = 90\°-\theta

\alpha = 90-59.72

\alpha = 30.27\°

Therefore the largest value of the angle α is 30.27°

3 0
3 years ago
When you look at a white light bulb through red sunglasses, why does the light look red to your eyes? What happened to all the o
Lelu [443]

Answer:

The answer is explained below in explanation

Explanation:

Whenever light falls on a colored surface, that color of light is reflected by the surface and all the other colors are absorbed. That is a black body appears black in all lights, because it absorbs every color and a white surface appears to be of the color of the light shone upon it because it is the mixture of all colors of light and reflects every color. The eyes only see the reflected light colors. The absorbed colors are not apparent to the eyes.

<u>Hence, when the white bulb is seen through red sunglasses, it does look like red to our eyes, while all the other colors are absorbed by the sun glasses.</u>

3 0
3 years ago
Please help with this problem. Thank you.​
4vir4ik [10]

Answer:

Explanation:

F = mω²R

F = 15(2π/8.5)²(7.8)

F = 63.93044788...

F = 63.9 N

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4 0
3 years ago
A package is pushed across the floor a distance of 90 feet by exerting a force of 32 lbs downward at an angle of 24 ∘ with the h
Crazy boy [7]

Answer:

2632 foot-pound

Explanation:

Work done: Work is said to be done when ever a force moves a body through a given distance. The S.I unit of force is Newton (N).

From the question,

The expression for work done is given as,

W = Fdcos∅......................... Equation 1

Where W = work done, F = force, d = distance, ∅ = angle between the force and the horizontal.

Given: F = 32 lbs, d = 90 feet, ∅ = 24°

substitute into equation 1

W = 32×90×cos24

W = 2880(0.914)

W = 2632.32

W = 2632 foot-pound

4 0
3 years ago
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