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Chapter 6: Q. 45 (page 156)

a. A rocket of mass mis launched straight up with thrust F鈫�thrust. Find an expression for the rocket鈥檚 speed at height hif air resistance is neglected.

b. The motor of a 350g model rocket generates9.5 N thrust. If air resistance can be neglected, what will be the rocket鈥檚 speed as it reaches a height of 85 m?

Short Answer

Expert verified

a). An expression for the rocket's speed at height hif the air is neglected localid="1649520749864" v=2Fthrust-mgmh

b). The speed of the rocket at height 85m is 54 m/s

Step by step solution

01

Part a). Step 1. Finding an expression

We can start solution with Newton's second law

ma=Fthrust-mga=Fthrust-mgm

Now, we can determine speed from an expression that includes acceleration and height

localid="1649520770861" v=2ahv=2路Fthrust-mgm路h

02

Part b) Step 1. Find the speed

Given that,m=0.35kgFthrust=9.5Nh=85mg=9.81m/s2

If we substitute values in the previous rocket's speed expression, we get

v=2脳(9.5-0.35脳9.81)0.35脳85=54.28鈮�54m/sapprox.

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Most popular questions from this chapter

Five balls move through the air as shown in FIGURE Q6.17 All five have the same size and shape. Air resistance is not negligible. Rank in order, from largest to smallest, the magnitudes of the accelerations aa to ae. Some may be equal. Give your answer in the form a7b=c7d7eand explain your ranking.

FIGURE Q6.17

At t=0, an object of mass mis at rest at x=0on a horizontal, frictionless surface. Starting at t=0, a horizontal forc茅 Fx=F0e鈭�t/Tis exerted on the object.

a. Find and graph an expression for the object's velocity at an arbitrary later time t.

b. What is the object's velocity after a very long time has elapsed?

A stubborn, 120 kg mule sits down and refuses to move. To drag the mule to the barn, the exasperated farmer ties a rope around the mule and pulls with his maximum force of 800 N. The coefficients of friction between the mule and the ground are ms = 0.8 and mk = 0.5. Is the farmer able to move the mule?

A construction worker with a weight of 850N stands on a roof that is sloped at 20掳. What is the magnitude of the normal force of the roof on the worker?
  1. Write a realistic problem for which these are the correct equations.
  2. Draw the free-body diagram and the pictorial representation for your problem.
  3. Finish the solution of the problem.
(100N)cos鈦�30鈭�鈭�fk=(20kg)ax

n+(100N)sin鈦�30鈭�鈭�(20kg)(9.80m/s2)=0fk=0.20n.
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