A 60 g particle is moving to the left at 24 m/s. How much work must be done on t

Question

A 60 g particle is moving to the left at 24 m/s. How much work must be done on the particle to cause it to move to the right at 33 m/s.

Basically, I have a hard time knowing when to add and when to subtract. Here is what I am thinking:

Work = change in kinetic energy = 1/2*m*v^2-1/2*m*v^2
So, 1/2*.06*24^2 = 17.20 J
1/2*.06*33^2=32.67
Work is the difference of kinetic energies, and since they are in opposite directions, I make one of them negative such that:

W = 17.2 minus negative 32.67
W = 49.87 J- Yes?

Explanation / Answer

Energy in = Energy out KE = KE + Work .5mv^2 = .5mv^2 + Work .5(.06)(24^2) = .5(.06)(33 - -24)^2) + Work Work = 1630.53 joules You need to find out how much the velocity changes..it goes from -24 to + 33 Therefore total change in v is 57m/s, which is what you have to use on the other side Hope this helps! Rate lifesaver :)

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