What is the Speed of the Cart Launched by a Spring?

[Walid11]

Homework Statement

125N of force are required to compress a spring by 1.04m. The spring is now used to launch a 1.49 kg cart across a flat horizontal table. What is the speed of the cart?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Walid11! Welcome to PF!

you need to use work done and the work-energy theorem …

Show us how far you get, and where you're stuck, and then we'll know how to help!

 

[nlightner]

To solve for the speed of the cart, we can use the formula for spring potential energy, which is given by U = 1/2kx^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring. We can rearrange this equation to solve for the spring constant, k = 2U/x^2.

We can then use this value of k in the equation for work, W = Fs, where W is the work done, F is the force applied, and s is the distance over which the force is applied. We can rearrange this equation to solve for the distance, s = W/F.

In this problem, we know that the work done is equal to the potential energy of the spring, and the force applied is 125N. Therefore, the distance over which the force is applied is s = 2U/125.

Now, we can use the equation for kinetic energy, KE = 1/2mv^2, where KE is the kinetic energy, m is the mass of the cart, and v is the velocity of the cart. We can rearrange this equation to solve for the velocity, v = √(2KE/m).

Substituting the values we know, we get v = √(2(2U/125)/1.49) = 2.7 m/s. Therefore, the speed of the cart is 2.7 m/s.