Proper significant digits please.
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Work can be calculated in two ways. It can be calculated as the dot product of force times displacement, and it can also be calculated as, generally speaking, the change in total energy of a system from one state to the next. To solve this, let's use the latter.
Kinetic Energy = 1/2 * m * v^2
Potential Energy = who cares, it's not used in this one.
KE0 = 4.0 kg*m^2/s^2 (and here, I've hidden some boring math).
KE1 = 9.0 kg*m^2/s^2 (again, hiding the math)
KE1 = KE0 + Work
9.0 = 4.0 + x (units are Joules, which are kg*m^2/s^2, btw)
x = 5.0 J.
Thus, the work done on the system is 5.0 Joules. The Work-Energy Theorem, as it's called, is useful for solving little problems like this in such a way that time doesn't enter into it.
Kinetic Energy = 1/2 * m * v^2
Potential Energy = who cares, it's not used in this one.
KE0 = 4.0 kg*m^2/s^2 (and here, I've hidden some boring math).
KE1 = 9.0 kg*m^2/s^2 (again, hiding the math)
KE1 = KE0 + Work
9.0 = 4.0 + x (units are Joules, which are kg*m^2/s^2, btw)
x = 5.0 J.
Thus, the work done on the system is 5.0 Joules. The Work-Energy Theorem, as it's called, is useful for solving little problems like this in such a way that time doesn't enter into it.
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W = delta K = K2 - K1
K2 = 1/2 m v2^2 = 1/2(2)(3)^2 = 9.0 J
K1 = 1/2 m v1^2 = 1/2(2)(2)^2 = 4.0 J
W = K2 - K1 = 9.0 J - 4.0 J = 5.0 J
The work done is 5.0 J
K2 = 1/2 m v2^2 = 1/2(2)(3)^2 = 9.0 J
K1 = 1/2 m v1^2 = 1/2(2)(2)^2 = 4.0 J
W = K2 - K1 = 9.0 J - 4.0 J = 5.0 J
The work done is 5.0 J