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Chapter 7: Q. 22 (page 178)

A $2.0 k g$ rope hangs from the ceiling. What is the tension at the midpoint of the rope?

Short Answer

Expert verified

The tension in the midpoint of the rope is $9.8 N$ .

Step by step solution

01

Given information

Mass of the rope $m = 2 k g$ .

02

Explanation

At the midpoint, the tension in the rope is supporting half the weight of the rope. For this, evaluateF and T

$F = m g \dots \dots (1)$

The tension at the midpoint localid="1649059361867" $T = \frac{F}{2} \dots \dots (2)$

Substituting the values in the equation $(1)$

localid="1649613472744" $F = (2 k g) (9.8 m / s^{2}) = 19.6 N$

Substituting the values in the equation $(2)$

localid="1649613456661" $T = \frac{19.6 N}{2} = 9.8 N$

The tension in the midpoint of the rope $T = 9.8 N$ .

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Most popular questions from this chapter

A $3200 k g$ helicopter is flying horizontally. A $250 k g$ crate is suspended from the helicopter by a massless cable that is constantly $20 °$ from vertical. What propulsion force F u prop is being provided by the helicopter’s rotor? Air resistance can be ignored. Give your answer in component form in a coordinate system where $\hat{i}$ points in the direction of motion and $\hat{j}$ points upward.

A $1000 k g$ car pushes a $2000 k g$ truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of $4500 N$ . Rolling friction can be neglected.

a. What is the magnitude of the force of the car on the truck?

b. What is the magnitude of the force of the truck on the car?

A steel cable lying flat on the floor drags a $20 k g$ block across a horizontal, frictionless floor. A $100 N$ force applied to the cable causes the block to reach a speed of $4 m / s$ in a distance of $2 m .$

What is the mass of the cable?

A 50-cm-diameter, 400 g beach ball is dropped with a 4.0 mg ant riding on the top. The ball experiences air resistance, but the ant does not. What is the magnitude of the normal force exerted on the ant when the ball’s speed is 2.0 m/s?

You find yourself in the middle of a frozen lake with a surface so slippery $(μ_{s} = μ_{k} = 0)$ you cannot walk. However, you happen to have several rocks in your pocket. The ice is extremely hard. It cannot be chipped, and the rocks slip on it just as much as your feet do. Can you think of a way to get to shore $?$ Use pictures, forces, and Newton's laws to explain your reasoning.

See all solutions

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