# Minimum compression of a spring.

A toy car with mass 0.043 kg is propelled by a spring with spring constant 92 N/m onto a track. The track contains a vertical loop of radius 0.15 m. Ignore any losses due to friction and use g = 10 m/s2. What is the minimum compression of the spring necessary for the car to complete the loop without leaving the track?

acceleration = velocity^2/radius= 10(0.15)= velocity^2
so v^2= 1.5

Then I use V to get KE = 1/2mv^2
KE= 1/2(0.043)(1.5)
KE= 0.03225

Add PE to the top of the loop PE = mgh
PE= (0.043)(10)(0.3)
PE=.0129

so then the Total E = PE + KE

TE = 1/2k x^2
PE+ KE= 1/2k x^2
.0129+ 0.03225= 1/2 (92) x^2
0.16125= 1/2 (92) x^2
0.3225 = 92x^2
0.003505 = x^2
x = minimum compression = 0.0592

Did i do everything correctly or is there a mistake somewhere?

## Answers and Replies

PhanthomJay
Science Advisor
Homework Helper
Gold Member
Add PE to the top of the loop PE = mgh
PE= (0.043)(10)(0.3)
PE=.0129 math error; PE = 0.129

Did i do everything correctly or is there a mistake somewhere?
Correct that simple math error and everything else looks OK.