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2 years ago

Three ropes A, B and C are tied together in one single knot K. (See figure.)

Physics

1 answer:

masha68 [24]2 years ago

6 0

The tension in the rope B is determined as 10.9 N.

<h3>Vertical angle of cable B</h3>

tanθ = (6 - 4)/(5 - 0)

tan θ = (2)/(5)

tan θ = 0.4

θ = arc tan(0.4) = 21.8 ⁰

<h3>Angle between B and C</h3>

θ = 21.8 ⁰ + 21.8 ⁰ = 43.6⁰

Apply cosine rule to determine the tension in rope B;

A² = B² + C² - 2BC(cos A)

B = C

A² = B² + B² - (2B²)(cos A)

A² = 2B² - 2B²(cos 43.6)

A² = 0.55B²

B² = A²/0.55

B² = 65.3/0.55

B² = 118.73

B = √(118.73)

B = 10.9 N

Thus, the tension in the rope B is determined as 10.9 N.

Learn more about tension here: brainly.com/question/24994188

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A luggage handler pulls a suitcase of mass 19.6 kg up a ramp inclined at an angle 24.0 ∘ above the horizontal by a force F⃗ of m

Dvinal [7]

(a) 638.4 J

The work done by a force is given by

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement of the object

$\theta$ is the angle between the direction of the force and the displacement

Here we want to calculate the work done by the force F, of magnitude

F = 152 N

The displacement of the suitcase is

d = 4.20 m along the ramp

And the force is parallel to the displacement, so $\theta=0^{\circ}$ . Therefore, the work done by this force is

$W_F=(152)(4.2)(cos 0)=638.4 J$

b) -328.2 J

The magnitude of the gravitational force is

W = mg

where

m = 19.6 kg is the mass of the suitcase

$g=9.8 m/s^2$ is the acceleration of gravity

Substituting,

$W=(19.6)(9.8)=192.1 N$

Again, the displacement is

d = 4.20 m

The gravitational force acts vertically downward, so the angle between the displacement and the force is

$\theta= 90^{\circ} - \alpha = 90+24=114^{\circ}$

Where $\alpha = 24^{\circ}$ is the angle between the incline and the horizontal.

Therefore, the work done by gravity is

$W_g=(192.1)(4.20)(cos 114^{\circ})=-328.2 J$

c) 0

The magnitude of the normal force is equal to the component of the weight perpendicular to the ramp, therefore:

$R=mg cos \alpha$

And substituting

m = 19.6 kg

g = 9.8 m/s^2

$\alpha=24^{\circ}$

We find

$R=(19.6)(9.8)(cos 24)=175.5 N$

Now: the angle between the direction of the normal force and the displacement of the suitcase is 90 degrees:

$\theta=90^{\circ}$

Therefore, the work done by the normal force is

$W_R=R d cos \theta =(175.4)(4.20)(cos 90)=0$

d) -194.5 J

The magnitude of the force of friction is

$F_f = \mu R$

where

$\mu = 0.264$ is the coefficient of kinetic friction

R = 175.5 N is the normal force

Substituting,

$F_f = (0.264)(175.5)=46.3 N$

The displacement is still

d = 4.20 m

And the friction force points down along the slope, so the angle between the friction and the displacement is

$\theta=180^{\circ}$

Therefore, the work done by friction is

$W_f = F_f d cos \theta =(46.3)(4.20)(cos 180)=-194.5 J$

e) 115.7 J

The total work done on the suitcase is simply equal to the sum of the work done by each force,therefore:

$W=W_F + W_g + W_R +W_f = 638.4 +(-328.2)+0+(-194.5)=115.7 J$

f) 3.3 m/s

First of all, we have to find the work done by each force on the suitcase while it has travelled a distance of

d = 3.80 m

Using the same procedure as in part a-d, we find:

$W_F=(152)(3.80)(cos 0)=577.6 J$

$W_g=(192.1)(3.80)(cos 114^{\circ})=-296.9 J$

$W_R=(175.4)(3.80)(cos 90)=0$

$W_f =(46.3)(3.80)(cos 180)=-175.9 J$

So the total work done is

$W=577.6+(-296.9)+0+(-175.9)=104.8 J$

Now we can use the work-energy theorem to find the final speed of the suitcase: in fact, the total work done is equal to the gain in kinetic energy of the suitcase, therefore

$W=\Delta K = K_f - K_i\\W=\frac{1}{2}mv^2\\v=\sqrt{\frac{2W}{m}}=\sqrt{\frac{2(104.8)}{19.6}}=3.3 m/s$

6 0

3 years ago

Two blocks are connected by a string over a pulley. The hanging block has a mass of 8-kg and the one on the plane has a mass of

jeka94

Answer:

Let f be force of friction on the blocks kept on inclined plane. T be tension in the string

For motion of block on the inclined plane in upward direction

T - m₁gsin40 - f = m₁a

f = μ m₁gcos40

For motion of hanging block on in downward direction

m₂g - T = m₂ a

Adding to cancel T

m₂g - - m₁gsin40 - μ m₁gcos40 = a ( m₁+m₂ )

a = g (m₂ - - m₁sin40 - μ m₁cos40) / ( m₁+m₂ )

Putting the values

a = 9.8 ( 4.75 - 2.12-1.045) / 7.6

2.04 m s⁻²

M₂ will go down and M₁ will go up with acceleration .

Explanation:

7 0

3 years ago

The distance between the centers of the wheels of a motorcycle is 156 cm. The center of mass of the motorcycle, including the ri

Drupady [299]

Answer:

a = 9.86 m/s²

Explanation:

given,

distance between the centers of wheel = 156 cm

center of mass of motorcycle including rider = 77.5 cm

horizontal acceleration of motor cycle = ?

now,

The moment created by the wheels must equal the moment created by gravity.

take moment about wheel as it touches the ground, here we will take horizontal distance between them.

then, take the moment around the center of mass. Since the force on the ground from the wheels is horizontal, we need the vertical distance.

now equating both the moment

m g d = F h

d is the horizontal distance

h is the vertical distance

m g d = m a h

term of mass get eliminated

g d = a h

so,

$a = \dfrac{g\ d}{h}$

$a = \dfrac{9.8\times 0.78}{0.775}$

a = 9.86 m/s²

4 0

3 years ago

A 1500kg car is at rest before it accelerates when the light turns green. If it covers 45.0 meters in 15.0 seconds, what is the

lana [24]

Answer:

300N

Explanation:

Given parameters:

Mass of car = 1500kg

Initial velocity = 0m/s

Distance covered = 45m

Time = 15s

Unknown:

Net force applied = ?

Solution:

From Newton's second law:

Force = mass x acceleration

Force = mass x $\frac{v - u}{t}$

v is the final velocity

u is the initial velocity

t is the time taken

Final velocity = $\frac{45}{15}$ =3m/s

Force = 1500 x $\frac{3 - 0}{15}$ = 300N

8 0

3 years ago

What type of matter will determine how much inertia an object has?

pshichka [43]

The two main things are speed and velocity. you have to factor in a bunch of smaller things too, but those don't really have much of an effect. And mass inertia is the resistance of any physical object to any change in its state of motion. The velocity of an object will determine the inertia that the object has. Good luck on your assignment and have a great day! :D

4 0

3 years ago