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By William Walton
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Additional resources for Collection of Problems in Illustration of the Principles of Theoretical Mechanics
Each clay pigeon has initial speed 30 ms"1 and acceleration 10 ms~2 downwards. How high above the ground do they collide? H A train accelerates along a straight, horizontal section of track. 5 m long, in a further 2 s. The motion of the train is modelled by assuming constant acceleration. Take the speed of the train when leaving the station to be t/ms" 1 and the acceleration to have the value a ms~ . (i) By considering the part of the journey from the station to the bridge, show that u + 4a = 15.
An equation involving uy v, a and s is required. The acceleration given is constant, a = -10; u = +5; v = 0 and s = H. 45 m. To find t\y given v = 0, a = —10 and u = +5 requires a formula in v, u, a and t. The ball takes half a second to reach its maximum height. 31 E (ii) Now consider the motion from the instant the first ball reaches the top of its path and the second is thrown up. Z. 13 Suppose that the balls have displacements above the origin of oc\ m and x2 m, as shown in the diagram, at a general time t s after the second ball is thrown up.
I) Draw diagrams showing the forces acting on (a) the book (b) the table as seen from the side. (ii) Write down equations connecting the forces acting on the book and on the table. 2 You balance a coin on your finger and move it up and down. The reaction of your ringer on the coin is R and its weight is W. Decide in each case whether R is greater than, less than or equal to W and describe the net force. (i) The coin is moving downwards with a constant velocity. (ii) The speed of the coin is increasing as it moves downwards.