A toy gun uses a spring with a force constant of 295 N/m to propel a 8.5-g steel

Question

A toy gun uses a spring with a force constant of 295 N/m to propel a 8.5-g steel ball. Assuming the spring is compressed 7.8 cm and friction is negligible, answer the following questions: What is the magnitude of the force, in newtons, that is needed to compress the spring? Numeric: A numeric value is expected and not an expression. What is the maximum height, in meters, to which the ball can be shot? Numeric: A numeric value is expected and not an expression. h_max = What is the gun's maximum range, in meters, on level ground? Numeric: A numeric value is expected and not an expression. R_max = A 110-g toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in the figure.

Explanation / Answer

Given that

spring constant K=295 N/m

mass of the ball m=8.5*10^-3 kg

compressed string length x=7.8 cm

basing on the concept of the work energy and power

now we find the force act on the compressed string

force F=KX=295*7.8*10^-2=23.01 N

now we find the maximum height ball can be shot

mgHmax=1/2kx^2

8.5*10^-3*9.8*Hmax=1/2*295*(0.078)^2

0.0833Hmax=0.8974

maximum height Hmax=10.8 m

now we find the range the ball can reach

range R=2Hmax=2*10.8=21.6 m

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