A simple mathematical model of a railway buffer consists of a horizontal open coiled spring attached to a fixed point. T

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A Simple Mathematical Model Of A Railway Buffer Consists Of A Horizontal Open Coiled Spring Attached To A Fixed Point T 3 (5.34 KiB) Viewed 36 times

A simple mathematical model of a railway buffer consists of a horizontal open coiled spring attached to a fixed point. The modulus of elasticity is 2×105Nm−1 and its natural length is 2 m. The buffer is designed to stop a railway truck before the spring is compressed to half its natural length, otherwise the truck will be damaged.
(i) Find the elastic energy stored in the spring when it is half its natural length. (ii) Find the maximum speed at which a truck of mass 2 tonnes can approach the buffer safely. Neglect any other reasons for loss of energy of the truck. A truck of mass 2 tonnes approaches the buffer at 5 ms−1. (iii) Calculate the minimum length of the spring during the subsequent period of contact. (iv) Find the thrust in the spring and the acceleration of the truck when the spring is at its minimum length. (v) What happens next?
(i) 5×104 J (ii) 7.07 ms−1 (iii) 1.29 m (iv) 7.07×104 N,35.4 ms−2 (v) Truck moves back along the rail at 5 ms−1 if other forces ignored.