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Chapter 9: Q.70 (page 230)

A 12kgweather rocket generates a thrust of 200N.The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550N/m, is anchored to the ground.

a. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?

b. After the engine is ignited, what is the rocket鈥檚 speed when the spring has stretched 40cm?

Short Answer

Expert verified

a. The compression in the spring is 21cm.

b. The speed of rocket is1.73m/s

Step by step solution

01

Content Introduction

The conservation of energy is

Ki+Ui+W=Kf+Uf+鈭�Eth

Considering the following diagram,

The origin of the coordinate system is placed on a free ed of the spring.

02

Explanation (Part a)

The rocket is initially at rest. Apply the newton's second law to balance the forces.

鈭�Fy=0Fsp-Fg=0Fsp=Fgk鈭�y=mg

Therefore,

鈭�y=mgk鈭�y=12kg(9.8m/s2)550N/m鈭�y=21cm

03

Explanation (Part b)

Use the equation for conservative energy wheny2-ye=40cmK2+Ug,2+Usp,2=K1+Ug,1+Usp,1+Wext12mv22+mgy2+12k(y2-ye)2=12mv12+mgy1+12k(y1-ye)212(12kg)v22+(12kg)(9.8m/s2)(40cm.1m100cm)+12(550N/m)(40cm.1m100cm)12(12kg)v22+47J+44J=-24J+11J+122Jv2=18J6kgv2=1.73m/s

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Most popular questions from this chapter

The motor of a crane uses power P to lift a steel beam. By what factor must the motor鈥檚 power increase to lift the beam twice as high in half the time?

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