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Chapter 7: Q.48 (page 180)

A 70 kg tightrope walker stands at the center of a rope. The rope supports are 10 m apart and the rope sags 10⁰ at each end. The tightrope walker crouches down, then leaps straight up with an acceleration of 8.0 m/s² to catch a passing trapeze. What is the tension in the rope as he jumps?

Short Answer

Expert verified

The tension in the rope as the tightrope walker jumps is $1612.45 N$

Step by step solution

01

Given information

mass of the tightrope walker $m = 70 k g$

The rope distance $= 10 m$

The acceleration of the tightrope walker to pass the catching trapezerole="math" localid="1649754268173" $a = g = 8 m / s^{2}$

The rope inclination $胃 = 10^{0}$

02

Explanation.

Free body Diagram for the given information is

From the above figure,

$\underset{i}{鈭�} F_{i, y} = 0$ we get

role="math" localid="1649754214901" $2 T \sin (胃) = W 鈬� T = \frac{m g}{2 \sin (胃)} = \frac{70 脳 8}{2 脳 \sin (10^{0})} = 1612.45 N$

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Most popular questions from this chapter

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of $6.0 k g$ , accelerates downward at $\frac{3}{4} g$ . What is the mass of the other block?

$F I G U R E C P 7.58$ shows three hanging masses connected by massless strings over two massless, frictionless pulleys.

a. Find the acceleration constraint for this system. It is a single equation relatinglocalid="1649865348893" $a_{1 y}, a_{2 y}, a n d a_{3 y} .$ Hint: $y_{A}$ isn鈥檛 constant.

b. Find an expression for the tension in string $A .$ Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns.

c. Suppose: $m_{1} = 2.5 k g, m_{2} = 1.5 k g, a n d m_{3} = 4.0 k g .$ Find the acceleration of each.

d. The $4.0 k g$ mass would appear to be in equilibrium. Explain why it accelerates.

A steel cable with mass is lifting a girder. The girder is speeding up.

a. Draw an interaction diagram.

b. Identify the 鈥渟ystem鈥� on your interaction diagram.

c. Draw a free-body diagram for each object in the system. Use

dashed lines to connect members of an action/reaction pair.

Your forehead can withstand a force of about $6.0 k N$ before fracturing, while your cheekbone can withstand only about $1.3 k N$ . Suppose a $140 g$ baseball traveling at $30 m / s$ strikes your head and stops in $1.5 m s$

a. What is the magnitude of the force that stops the baseball?

b. What force does the baseball exert on your head? Explain.

c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?

A $40 c m$ diameter, $50 c m$ tall, $15 kg$ hollow cylinder is placed on top of a $40 c m$ -diameter, $30 c m$ -tall, $100 kg$ cylinder of solid aluminum, then the two are sent sliding across frictionless ice. The static and kinetic coefficients of friction between the cylinders are $0.45$ and $0.25$ , respectively. Air resistance cannot be neglected. What is the maximum speed the cylinders can have without the top cylinder sliding off?

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