Assuming negligible friction,what spring constant (force constant)would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m?
A)20 N/cm
B)200 N/m
C)2000 N/cm
D)0.0020 N/m

Question

Quizplus · Accepted Answer

To find the spring constant (k), we use energy conservation principles. The potential energy stored in the spring (1/2 k x^2) when compressed is converted into gravitational potential energy (mgh) at the peak of the pellet's trajectory. Given: m = 0.01 kg (10 g converted to kg), g = 9.8 m/s^2 (acceleration due to gravity), h = 100 m, and x = 0.10 m. Rearranging the energy conservation equation 1/2 k x^2 = mgh for k gives k = 2mgh / x^2. Plugging in the values gives k = 2*0.01*9.8*100 / 0.10^2 = 1960 N/m, which when converted to N/cm (by dividing by 100) gives 19.6 N/cm, rounding to 20 N/cm.

Assuming Negligible Friction,what Spring Constant (Force Constant)would Be Needed by the Spring