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2 years ago

Consider the static equilibrium diagram here. What is the angle F1 must make with the horizontal?

Physics

2 answers:

Nataly [62]2 years ago

4 0

ANSWER

$\theta=35\degree$

EXPLANATION

Since the body is in equilibrium, total upward forces must equal total downward force.

Also the net horizontal forces acting on the body must be zero.

We need to resolve $F_1$ into vertical and horizontal components.

The horizontal component is

$x=F_1\cos\theta$ .

The vertical component is

$y=F_1\sin\theta$ .

Equating the up force to the downward forces gives,

$F_1\sin\theta + 20N=60N$ .

This implies that,

$F_1\sin\theta =60N-20N$ .

$F_1\sin\theta=40N...eqn1$

Also the horizontal forces must be equal.

$F_1\cos\theta=57N...eqn2$ .

Dividing equation (1) by equation (2) gives,

$\frac{F_1\sin\theta}{F_1\cos\theta}=\frac{40}{57}$ .

$\Rightarrow \tan\theta=0.70175$

$\Rightarrow \theta=tan^{-1}(0.70175)$

$\Rightarrow \theta=35.0594$ .

Therefore the given angle that $F_1$ must make with the horizontal is approximately 35° to the nearest degree.

suter [353]2 years ago

4 0

A. 35 on plato, got 100 on the test :)

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A driver's foot presses with a steady force of 20N on a pedal in a car as shown.

azamat

Answer:

160N

Explanation:

Moments must be conserved - so.

$20 * 0.4 = F * 0.05$

$F=\frac{20*0.4}{0.05} = 160$

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2 years ago

the brightest , hottest, and most massive stars are the brilliant blue stars designated as spectral class O. if a class O star w

4vir4ik [10]

The speed is 0.956 m / s.

<u>Explanation</u>:

The kinetic energy is equal to the product of half of an object's mass, and the square of the velocity.

K.E = 1/2 $\times$ m $\times$ $v^{2}$

where K.E represents the kinetic energy,

m represents the mass,

v represents the velocity.

K.E = 1/2 $\times$ m $\times$ $v^{2}$

1.10 $\times$ 10^42 = 1/2 $\times$ 3.26 $\times$ 10^31 $\times$ $v^{2}$

$v^{2}$ = (1.10 $\times$ 10^42 $\times$ 2) / (3.26 $\times$ 10^31)

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2 years ago

A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point loc

Dafna11 [192]

Answer:

(a) 18.75 rad/s²

(b) 14920.78 rev

Explanation:

(a)

First we find the acceleration of the centrifuge using,

a = (v-u)/t......................... Equation 1

Where v = final velocity, u = initial velocity, t = time.

Given: v = 150 m/s, u = 0 m/s ( from rest), t = 100 s

Substitute into equation 1

a = (150-0)/100

a = 1.5 m/s²

Secondly we calculate for the angular acceleration using

α = a/r..................... Equation 2

Where α = angular acceleration, r = radius of the centrifuge

Given: a = 1.5 m/s², r = 8 cm = 0.08 m

substitute into equation 2

α = 1.5/0.08

α = 18.75 rad/s²

(b)

Using,

Ф = (ω'+ω).t/2........................... Equation 3

Where Ф = number of revolution of the centrifuge, ω' = initial angular velocity, ω = Final angular velocity.

But,

ω = v/r and ω' = u/r

therefore,

Ф = (u/r+v/r).t/2

where u = 0 m/s (at rest), = 150 m/s, r = 0.08 m, t = 100 s

Ф = [(0/0.08)+(150/0.08)].100/2

Ф = 93750 rad

If,

1 rad = 0.159155 rev,

Ф = (93750×0.159155) rev

Ф = 14920.78 rev

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2 years ago

A bicycle rider has a speed of 19.0 m/s at a height of 55.0 m above sea level when he begins coasting down hill. The mass of the

lukranit [14]

Answer:

The mechanical energy of the rider at any height will be 6.34 × 10⁴ J.

Explanation:

Hi there!

The mechanical energy of the rider is calculated as the sum of the gravitational potential energy plus the kinetic energy. Since there are no dissipative forces (like friction), the mechanical energy of the rider at a height of 55.0 m above the sea level will be the same at a height of 25.0 m (or at any height), because the loss in potential energy will be compensated by a gain in kinetic energy, according to the law of conservation of energy.

Then, calculating the potential and kinetic energy at 55.0 m and 19 m/s, we can obtain the mechanical energy that will be constant:

Mechanical energy = PE + KE

Where:

PE = potential energy.

KE = kinetic energy.

The potential energy is calculated as follows:

PE = m · g · h

Where:

m = mass of the object.

g = acceleration due to gravity.

h = height.

Then, the potential energy of the rider will be:

PE = 88.0 kg · 9.81 m/s² · 55.0 m = 4.75 × 10⁴ J

The kinetic energy is calculated as follows:

KE = 1/2 · m · v²

Where "m" is the mass of the object and "v" its velocity. Then:

KE = 1/2 · 88.0 kg · (19.0 m/s)²

KE = 1.59 × 10⁴ J

The mechanical energy of the rider will be:

Mechanical energy = PE + KE = 4.75 × 10⁴ J + 1.59 × 10⁴ J = 6.34 × 10⁴ J

This mechanical energy is constant because when the rider coast down the hill, its potential energy is being converted into kinetic energy, so that the sum of potential energy plus kinetic energy remains constant.

5 0

1 year ago

When the sun’s rays are at an angle of 39°, the distance from the top of Dakota’s head to the tip of her shadow is 77 inches. Ab

slavikrds [6]

Answer:

Dakota is 48 inches tall.

Explanation:

We can solve this problem using trigonometry. Since the angle between Dakota and the ground is nearly 90°, we can construct a rectangle triangle, whose sides are Dakota, her shadow, and the distance between the top of her head to the tip of her shadow. Let the Dakota's height be D. Since the angle between the sun's rays and the ground is 39° and the distance between the tip of her shadow and Dakota's head is 77 inches, we can state that:

$\sin39\°=\frac{D}{77"}\\\\\implies D=77"\sin39\°\\\\D=48"$

So, this means that Dakota is 48 inches tall.

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1 year ago