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Q. 73

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 63

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Short Answer

Your goal in the laboratory is to launch a ball of mass m straight up so that it reaches exactly the height h above the top of the launching tube. You and your lab partners will earn fewer points if the ball goes too high or too low. The launch tube uses compressed air to accelerate the ball over a distance d, and you have a table of data telling you how to set the air compressor to achieve the desired acceleration. Find an expression for the acceleration that will earn you maximum points

The acceleration of the ball to earn maximum points is hdg

See the step by step solution

Step by Step Solution

Step 1. To write the given information,

The maximum height the ball should reach is hThe distance that the launching tube can accelerate is dSince the ball is thrown upwards, the final velocity is vf=0 m/sLet the initial velocity is viThe acceleration of the ball is aThe acceleration due to gravity is gThe time taken by the ball to reach height is t

Step 2. To determine the acceleration of the ball

Write the equation of motion for the ball thrown above for the maximum height h,

h=12gt2t2=2hg .....(1)

Write the equation of motion to determine the initial velocity of the ball,

vf=vi+at0=vi-gtvi= gt ......(2)

Write the equation of motion to determine the acceleration,

localid="1648616761150" vf2-vi2= 2ad0-vi2= 2ad ......(3)

Plug the value vi from equation (2)gt2=2adg2t2= 2ad ......(4)Substitute the value of t2 form equation (1)

g22hg= 2ad2gh= 2ada=hdg

Therefore the acceleration of the ball to earn maximum points is hdg

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