Minimum compression of a spring.

[college boy19]

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?

 

[PhanthomJay]

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.

 

[nlightner]

Your calculations and approach seem correct. However, it is always a good idea to double check your work and make sure you are using the correct units for each calculation. Also, it would be helpful to include units in your final answer, so the minimum compression of the spring would be 0.0592 m.