Parts a-c (6%) Problem 13. A toy gun uses a spring with a force constant of 315
ID: 2031883 • Letter: P
Question
Parts a-c
(6%) Problem 13. A toy gun uses a spring with a force constant of 315 Nm to propel a 8.5-g steel ball. Assuming the spring is compressed 7.7 cm and friction is negligible, answer the following questions: 33% Part (a) What is the magnitude of the force, in newtons, that is needed to compress the spring? Gra Ded Poter tan( ) acos( Subr Atter (090 deta sin() cosO asin atan acotansinh0 cosh)tanh) cotanh T cotan END Degrees Radians BACKSPACE DEL CLEAR Submit Hint I give up! Hints: 2% deduction per hint. Hints remaining: 1 Feedback: 2% deduction per feedback. 33% Part (b) What is the maximum height, in meters, to which the ball can be shot? -là 33% Part (c) What is the gun's maximum range, in meters, on level ground?Explanation / Answer
a)
Force needed to compress the spring
F=KX=315*0.077=24.255 N
b)
By conservation of energy
(1/2)Kx2=mgh
(1/2)*315*0.0772 =0.0085*9.81*h
h=11.2 m
c)
By conservation of energy
(1/2)Kx2=(1/2)mV2
315*0.0772=0.0085*V2
V=14.823 m/s
Range
R=V2/2g =14.8232/9.81
R=22.4 m