Question

A cumin canister of mass m= 0.40kg slides across a horizontal frictionless counter with speed v=0.50 m/s. It then runs into and compresses a spring of spring constant k=750 N/m. When the canister is

momentarily stopped by the spring, by what distance d is the spring compressed. The explanation the text book implicitly gives is that the change in kinetic energy of the canister is equal to the Work done on the canister by the spring. This makes sense but in the previous page the textbook logically states that total change in kinetic energy= Wa (work done by applied force) and Ws (work done by spring force). This statement also makes sense. The book also states that change in kinetic energy is moving if the block attached to a spring was stationary before and after work was done on it. This also makes sense since Vo=V=0. What I'm having trouble understanding is how the textbook used the equation for total change in kinetic energy (stated above) to set the kinetic energy of the canister = to the work done by spring. This chapter does not discuss potential energy which is explored in the next chapter. My initial reaction to this question was to set total change in kinetic energy= Wa +Ws= -1/2mv^2 - 1/2kd^2 but this approach is clearly wrong. Any help would be greatly appreciated.