# 4.7 Further applications of newton’s laws of motion  (Page 6/6)

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A cartoon shows the toupee coming off the head of an elevator passenger when the elevator rapidly stops during an upward ride. Can this really happen without the person being tied to the floor of the elevator? Explain your answer.

## Problem exercises

A flea jumps by exerting a force of $1\text{.}\text{20}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{N}$ straight down on the ground. A breeze blowing on the flea parallel to the ground exerts a force of $0\text{.}\text{500}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{N}$ on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is $6\text{.}\text{00}×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{kg}$ . Do not neglect the gravitational force.

$\text{10.2}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\text{, 4.67º from vertical}$

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in [link] . (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

A 76.0-kg person is being pulled away from a burning building as shown in [link] . Calculate the tension in the two ropes if the person is momentarily motionless. Include a free-body diagram in your solution.

${T}_{1}=\text{736 N}$

${T}_{2}=\text{194 N}$

Integrated Concepts A 35.0-kg dolphin decelerates from 12.0 to 7.50 m/s in 2.30 s to join another dolphin in play. What average force was exerted to slow him if he was moving horizontally? (The gravitational force is balanced by the buoyant force of the water.)

Integrated Concepts When starting a foot race, a 70.0-kg sprinter exerts an average force of 650 N backward on the ground for 0.800 s. (a) What is his final speed? (b) How far does he travel?

(a) $7.43 m/s$

(b) 2.97 m

Integrated Concepts A large rocket has a mass of $2\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{kg}$ at takeoff, and its engines produce a thrust of $3\text{.}\text{50}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{N}$ . (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust? (c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

Integrated Concepts A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.

(a) $4.20 m/s$

(b) $\text{29.4}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$

(c) $4\text{.}\text{31}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$

Integrated Concepts A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m. (a) Neglecting air resistance (a poor assumption, but we will make it for this example), calculate the shell’s velocity when it leaves the mortar. (b) The mortar itself is a tube 0.450 m long. Calculate the average acceleration of the shell in the tube as it goes from zero to the velocity found in (a). (c) What is the average force on the shell in the mortar? Express your answer in newtons and as a ratio to the weight of the shell.

Integrated Concepts Repeat [link] for a shell fired at an angle $\text{10.0º}$ from the vertical.

(a) 47.1 m/s

(b) $2\text{.}\text{47}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$

(c) $6.18×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$ . The average force is 252 times the shell’s weight.

Integrated Concepts An elevator filled with passengers has a mass of 1700 kg. (a) The elevator accelerates upward from rest at a rate of $1\text{.}{\text{20 m/s}}^{2}$ for 1.50 s. Calculate the tension in the cable supporting the elevator. (b) The elevator continues upward at constant velocity for 8.50 s. What is the tension in the cable during this time? (c) The elevator decelerates at a rate of $0\text{.}{\text{600 m/s}}^{2}$ for 3.00 s. What is the tension in the cable during deceleration? (d) How high has the elevator moved above its original starting point, and what is its final velocity?

Unreasonable Results (a) What is the final velocity of a car originally traveling at 50.0 km/h that decelerates at a rate of $0\text{.}{\text{400 m/s}}^{2}$ for 50.0 s? (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

Unreasonable Results A 75.0-kg man stands on a bathroom scale in an elevator that accelerates from rest to 30.0 m/s in 2.00 s. (a) Calculate the scale reading in newtons and compare it with his weight. (The scale exerts an upward force on him equal to its reading.) (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?

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