Answer:
1.93 m/s
Explanation:
Parameters given:
Mass = 4.5g = 0.0045kg
Spring constant = 8.0 N/m
Length of barrel = 13 cm = 0.013m
Frictional force = 0.035N
Compression = 5.8 cm = 0.058m
First, we find the P. E. stored in the spring:
P. E. = ½*k*x²
P. E. = ½ * 8 * 0.058² = 0.013J
Then, we find the work done by the frictional force while the sphere is leaving the barrel of the gun:
Work = Force * distance
The distance here is the length of the barrel.
Work = 0.035 * 0.13 = 0.0046 J
The kinetic energy of the sphere can now be found:
K. E. = P. E. - Work done
K. E. = 0.013 - 0.0046 = 0.0084J
We can now find the speed using the formula for K. E.:
K. E. = ½*m*v²
0.0084 = ½ * 0.0045 * v²
v² = 0.0084/0.00255 = 3.733
=> v = 1.93 m/s
