13 A diving board of length 5.0 m is hinged at one end and supported 2.0 m from this end by a springof spring constant 10 kN m–1. A child of mass 40 kg stands at the far end of the board.mass of child40 kg2.0 m5.0 mdiving boardspring hingeWhat is the extra compression of the spring caused by the child standing on the end of theboard?A 1.0 cm B 1.6 cm C 9.8 cm D 16 cm
Question
13 A diving board of length 5.0 m is hinged at one end and supported 2.0 m from this end by a springof spring constant 10 kN m–1. A child of mass 40 kg stands at the far end of the board.mass of child40 kg2.0 m5.0 mdiving boardspring hingeWhat is the extra compression of the spring caused by the child standing on the end of theboard?A 1.0 cm B 1.6 cm C 9.8 cm D 16 cm
Solution
To solve this problem, we need to use the principle of moments. The principle of moments states that the sum of the moments about any point in a system is equal to the sum of the moments about any other point in the system.
Step 1: Calculate the moment caused by the child. The moment (M) is calculated by multiplying the force (F) by the distance (d) from the pivot point. The force is the weight of the child, which is the mass (m) times gravity (g). So, M = m * g * d.
In this case, the mass of the child is 40 kg, gravity is approximately 9.8 m/s^2, and the distance from the pivot point (the hinge) to the child is 5.0 m. So, M = 40 kg * 9.8 m/s^2 * 5.0 m = 1960 Nm.
Step 2: Calculate the extra compression of the spring. The moment caused by the spring is also calculated by multiplying the force by the distance from the pivot point. However, in this case, the force is the spring force, which is the spring constant (k) times the compression (x). So, M = k * x * d.
We know the moment (M) is 1960 Nm, the spring constant (k) is 10 kN/m = 10000 N/m, and the distance from the pivot point to the spring (d) is 2.0 m. We can solve for the compression (x) by rearranging the equation to x = M / (k * d).
So, x = 1960 Nm / (10000 N/m * 2.0 m) = 0.098 m = 9.8 cm.
Therefore, the extra compression of the spring caused by the child standing on the end of the board is 9.8 cm. So, the correct answer is C.
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