physics question- springs pt 2

Question

A toy car with mass of m=136 GRAMS crashes into a spring with constant k=37 N/m. If the car was going v=1.93 m/s, then how far will the spring compress? In your answer:
respond in terms of meters. Do not put your answer in terms of cm or any other unit of length.

 

please help :) thank you!

Answer 1

Hi!  This problem, like the other one I answered, makes use of the formula for potential energy stored in a spring:  PE=0.5kx^2

 

For this formula to give us a potential energy in Joules, the spring constant (k) needs to be in units of Newtons per meter, and the distance of compression (x) needs to be in units of meters.

 

In this problem, the kinetic energy that the toy car initially had is what gets stored in the spring, so let's find the car's initial kinetic energy using the formula KE=0.5mv^2.  For this formula to give us a KE in Joules, m needs to be in kilograms and v needs to be in meters per second.  The mass of the car is 0.136 kg (let me know if you're not confident with unit conversions--I can help with that, too!), so when we plug all the numbers in, we get KE=0.5*0.136*1.93^2, or 0.253 J.

 

Now that we know the spring is going to end up storing 0.253 J, let's apply the formula for potential energy stored in a spring:  PE=0.5kx^2.  If we plug in all the numbers, we get 0.253=0.5*37*x^2.  Solving that, we get 0.0137 = x^2, so x=0.117 m.

 

Please let me know if you have any questions or comments about this, or if you'd like to schedule one or more online tutoring sessions!  I teach physics, math, and a wide variety of other subjects.