To calculate the spring constant of the slingshot, we can use Hooke's Law and the equation F = k * x, where F is the force, k is the spring constant, and x is the displacement. By substituting the given values into the equation, we can solve for k and find that the spring constant of the slingshot is 78.4 N/m.
To calculate the spring constant of the slingshot, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. First, we need to find the force exerted by the slingshot on the watermelon, which can be calculated using the equation: F = k * x, where F is the force, k is the spring constant, and x is the displacement. In this case, the displacement is the distance the slingshot is pulled bacwhich is 1.5 m. The force exerted on the watermelon is its weight, which is given by the equation: F = m * g, where m is the mass of the watermelon and g is the acceleration due to gravity. Therefore, we have m * g = k * x, where m = 12 kg, g = 9.8 m/s², and x = 1.5 m. Solving for k, we get k = (m * g) / x = (12 kg * 9.8 m/s²) / 1.5 m = 78.4 N/m.