Which of the following is an arithmetic sequence? A. 2, 1, 4, 3, 6, 5, …

A 26.4 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the ca

MA_775_DIABLO [31]

Answer:

The horizontal component of the force exerted by the hinge on the beam is 47.15 N.

Explanation:

Given data:

Weight of beam = 26.4 kg

Angle between the beam and the cable is 90°

Beam inclination with respect to horizontal with an angle, $\theta = 23.4\°$

<u>We need to find the horizontal component of the force exerted by the hinge on the beam.</u>

Solution:

Let 'L' be length of the beam, 'T' be tension in the cable , $F_{h}$ be horizontal component of force by the hinge, and $F_{v}$ be vertical component of force by the hinge.

Take counterclockwise torque as positive.

Let us find torques around the hinge.

Torque by tension is given as:

$\tau = T \times L$

Torque by the force of gravity is given as:

$\tau_g= m g \frac{L}{2}\times cos \theta$

Torques by $F_{h}$ and $F_{v}$ are 0 as they act on the hinge itself.

Now, for equilibrium, net torque about the hinge is 0. So,

$\tau-\tau_g=0$

$T L - m g \frac{L}{2}\times \cos(\theta) = 0$

Dividing both sides by 'L', we get:

$T - m \frac{g}{2}\times \cos \theta = 0$

$T=m \frac{g}{2} \times cos \theta$ --------------------(1)

As per question, the cable makes 90° with the horizontal.

So, the net horizontal force is also zero. Therefore,

$F_{h} -T cos(90- \theta) = 0$

$F_h - T sin(\theta) = 0$

$F_h = T sin(\theta)$ --------------------------(2)

Plug the value of 'T' from equation (1) into equation (2). This gives,

$F_{h} = m \frac{g}{2} \times cos \theta \times sin \theta$

$F_{h} = 26.4 \times \frac{9.8}{2} \times cos(23.4) \times sin(23.4)$

$F_{h} = 47.15\ N$

Therefore, the horizontal component of the force exerted by the hinge on the beam is 47.15 N.

3 0

3 years ago

The equation for the speed of a satellite in a circular orbit around the earth depends on mass. Which mass?

katovenus [111]

<h3><u>Question: </u></h3>

The equation for the speed of a satellite in a circular orbit around the Earth depends on mass. Which mass?

a. The mass of the sun

b. The mass of the satellite

c. The mass of the Earth

<h3><u>Answer:</u></h3>

The equation for the speed of a satellite orbiting in a circular path around the earth depends upon the mass of Earth.

Option c

<h3><u> Explanation: </u></h3>

Any particular body performing circular motion has a centripetal force in picture. In this case of a satellite revolving in a circular orbit around the earth, the necessary centripetal force is provided by the gravitational force between the satellite and earth. Hence $F_{G} = F_{C}$ .

Gravitational force between Earth and Satellite: $F_{G} = \frac{G \times M_e \times M_s}{R^2}$

Centripetal force of Satellite : $F_C = \frac{M_s \times V^2}{R}$

Where G = Gravitational Constant

$M_e$ = Mass of Earth

$M_s$ = Mass of satellite

R= Radius of satellite’s circular orbit

V = Speed of satellite

Equating $F_G = F_C$ , we get

Speed of Satellite $V =\frac{\sqrt{G \times M_e}}{R}$

Thus the speed of satellite depends only on the mass of Earth.

6 0

3 years ago

A cannon fires a 0.652 kg shell with initial

laila [671]

Mass have no effect for the projectile motion and u want to know the height "h"
first,
find the vertical and horizontal components of velocity
vertical component of velocity = 12 sin 61
horizontal component of velocity = 12 cos 61
now for the vertical motion ;
S = ut + (1/2) at^2
where
s = h
u = initial vertical component of velocity
t = 0.473 s
a = gravitational deceleration (-g) = -9.8 m/s^2

h=[12×sin 610×0.473]+[−9.8×(0.473)2]

u can simplify this and u will get the answer

h=.5Gt2

H=1.09m

6 0

3 years ago

Read 2 more answers

Which statement correctly describes the relationship between thermal energy and particle movement?

zhuklara [117]

As thermal energy increases, there is more particle movement. As thermal energy increases, there is more particle movement. As thermal energy increases, there is less particle movement.

Sure hope this helps you

5 0

2 years ago

Help me on question 5

Sveta_85 [38]

I believe it is acceleration!

6 0

3 years ago

Read 2 more answers