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Chapter 6: Q.39 (page 156)

The 1000 kg steel beam is supported by two ropes. What is the tension in each?

Short Answer

Expert verified

Tension in rope 1 is $6035.5 N$

Tension in rope 2 is $4128.5 N$

Step by step solution

01

Given information

Weight of beam- $= 1000 K G$

Angle between rope $1$ and perpendicular is $20 掳$

Angle between rope $2$ and perpendicular is $30 掳$

02

Assumptions

Let rope $1$ be $R 1$ and rope $2$ be $R 2 .$

Tension of rope 1 $= T R 1$

Tension of rope 2 $= T R 2$

Point $0 (m g)$ is where two ropes are connected.

03

Calculation of tension in each rope

$A t p o i n t 0$

${鈭�}_{}^{} f x = 0$

localid="1649397086445" $T R_{1} \sin (20 掳) =$ localid="1649397058574" $T R_{2} \sin (30 掳)$

localid="1649614498151" $T R_{2} =$ localid="1649614527752" role="math" $2 脳 T_{R 1}$ localid="1648026003669" $\sin (20 掳)$ $鈥� e q . 1$

${鈭�}_{}^{} f x = 0$

localid="1649614427856" $T R_{1} \cos (30)$ $+$ localid="1649396955821" $T R_{2} \cos (30 掳)$ $= m g$

localid="1649396975732" $T R_{1} \cos (20 掳) + 2 T R_{1} \sin (20 掳)$ $= 1000$ $脳 9.8$

Tension in rope 1

$T R_{1}$ is $6035.5 N$

Tension in rope 2 $T R_{2}$ -

localid="1649397189749" $T R_{2} =$ localid="1649396688322" $2 脳 6035.5 脳 \sin 20 掳$

Tension in rope 2

$T R_{2}$ is $4128.5 N$

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Most popular questions from this chapter

A $2.0 k g$ object initially at rest at the origin is subjected to the time-varying force shown in the figure. What is the object鈥檚 velocity at $t = 4 s$ ?

An object moving in a liquid experiences a linear drag force: ${\overset{鈫�}{F}}_{drag} = (b v$ , direction opposite to the motion), where $b$ is a constant called the drag coefficient. For a sphere of radius $R,$ the drag constant can be computed as $b = 6 蟺畏 R$ , where $畏$ is the viscosity of the liquid.

a. Find an algebraic expression for $v_{x} (t)$ , the $x$ -component as a function of time, for a spherical particle of radius $R$ and mass $m$ that is shot horizontally with initial speed $v_{0}$ through a liquid of viscosity $畏$ .

b. Water at $20 掳 C$ has viscosity $畏 = 1.0 脳 10^{- 3} N s / m^{2}$ . Suppose a $4.0 - c m$ -diameter, $33 g$ ball is shot horizontally into a tank of $20 掳 Cl$ water. How long will it take for the horizontal speed to decrease to $50 %$ of its initial value?

A rubber-wheeled $50 k g$ cart rolls down a $15 掳$ concrete incline. What is the cart鈥檚 acceleration if rolling friction is

(a) neglected and

(b) included?

Are the objects described here in equilibrium while at rest, in equilibrium while in motion, or not in equilibrium at all? Explain.

a. A 200 pound barbell is held over your head.

b. A girder is lifted at constant speed by a crane.

c. A girder is being lowered into place. It is slowing down.

d. A jet plane has reached its cruising speed and altitude.

e. A box in the back of a truck doesn鈥檛 slide as the truck stops.

A block of mass $m$ is at rest at the origin at $t = 0$ . It is pushed with constant force $F_{0}$ from $x = 0$ to $x = L$ across a horizontal surface whose coefficient of kinetic friction is $渭_{k} = 渭_{0} (1 鈭� x / L)$ . That is, the coefficient of friction decreases from $渭_{0}$ at $x = 0$ to zero at $x = L$ .

a. Use what you've learned in calculus to prove that

$a_{r} = v_{r} \frac{d v_{x}}{d x}$

b. Find an expression for the block's speed as it reaches position $L$ .

See all solutions

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