 # Classical Mechanics Questions

## Transcribed Text

Q1.) As we will soon discover in this course, an object moving in a circular path with constant speed is said to experience a centripetal acceleration, aC. Use dimensional analysis to deduce an equation for the centripetal acceleration. Begin by assuming that this acceleration might relate to the mass of the object, m, the radius of the circular path, r and the speed of the object, v. Hint: You may assume that the units for centripetal acceleration are the same as for the linear acceleration we have seen already. Q2.) During lecture, Prof. Dean demonstrates the motion of a body under earth’s gravity by tossing a small ball straight up in the air. Unsurprisingly, the ball first rises some distance, then falls to the floor. Assume that the ball leaves the professors hand from a hegiht of 3/2 m above the floor, and that when release the ball is travelling at a speed of 2 m/s. a) When the ball reaches its maximum height, what will be its velocity and its acceleration? b) What is the maximum height reached (take acceleration due to gravity to have magnitude 9.8 m/s2)? c) Once the ball hits the ground, what will have been its total displacement? d) What is the velocity when the chalk hits the ground? e) Plot on three separate graphs the displacement, velocity and acceleration of the ball versus time. Q3.) A Hare and a Tortoise enter into a race, each outfitted with jet propulsion engines of their own design. The Hare designs an engine that can accelerate at a whopping 10 m/s2, and reach a maximum speed of 10 m/s. The Tortoise’s engine accelerates at only 2 m/s, but can reach speeds of 20 m/s, twice that of the Hare. They agree to race a distance of 100 m. a) Calculate the time to complete the race for both the Tortoise and the Hare. b) On the same graph, sketch the displacement versus time for Tortoise and the Hare. Do the same for the velocity and the acceleration. Pizza vDrone hD hC d Figure 1 Q4.) A local pizza shop decides to use drones for their delivery. The drone flies along a horizontal path parallel to the ground, at a height of hD = 6.9 m, and with speed of 2 m/s. If the drone were to drop the pizza without stopping (see Fig.) a) At what distance, d, from the waiting customer should the drone release the pizza box so that it lands precisely in the hands of the customer? Assume the outstretched arms of the customer are at height of hC = 2 m to the ground. b) What is the velocity of the box when it reaches the customer? c) What is its speed at this point? 1

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