work done by tugboat = 6000 * 4000
= 24 * 10^6 Joules
work done by water = -500*4000 = -2*10^6 Joules (negative because force is opposite to motion)
net work done on ship = 22*10^6 Joules
Note unbalanced force on ship leads to acceleration but we do not care.
a Joule is a Newton meter
which is
kg meter/s^2 * meter = kg meter^2/s^2
A tugboat pulls a ship with a constant horizontal force of 6000N and causes the ship to move through a harbor. The water exerts a constant drag force on the ship of 500N. How much work is done on the ship if it moves a distance of 4.0 km?
Force is causing parallel displacement. Work is done by boat. Work by boat is acting positively. The boat has kinetic energy by moving forward on it's own. Work has no potential. Is work by kinetic energy is (0.5)mv^2? But I don't know the mass. I know the exerted force is 6000. Force is mass and acceleration. If force is the dividend of acceleration, I could find mass of boat. But what is acceleration? change in velocity partitioned by the time of change. But what is velocity? It is not given. Go back. Perhaps the belief that work is done by KE is erroneous or irrelevant? (Which is it?) Without the knowledge of speed, rate of change, and mass, how can we find out what work is? What is work? Well it's measured in joules... What is a joule? Ah, something like force partitioned by time. What is force? Some newtons. What is time? Some seconds. (SI units). So to know Work, is to know partitioned newtons of force. I know That the boat is exerting 6000 newtons in a (assumed) parallel direction of displacement. Parallel as in, 100% of the force is delivered in displacement. We have 100% of displacement. What is displacement? 4.0 km. 100% of 4.0km is 4.0km. So 6000 Newtons of force is delivered 4.0 (km). For 4.0 (km), 6000 newtons of force has been delivered. 4.0 (km) and 6000 (N) form a product of [24,000 (km)(N)]
A newton is the product of 1 kg with the quotient of the displacement (SI meter) partitioned by a squared second. A newton is the product of 1 kg and an acceleration; the product of mass and acceleration.
The product, 24,000, should have units kg, m, and s. This product does not have these units. The multiplicand, displacement of the boat was measured in km. 4.0 km is simply 4 thousand meters. To correct my mistake, 4,000 (meters) and 6,000 (newtons) form the product 2.4(10^7) [1kg(m^2)/(s^2)]
Because the nature of this product's units is such that mass, displacement, and time intertwine, these units make up the joule. The product is 2.4(10^7) Joules. 2.4(10^7) Joules of work by Kinetic Energy so I have not made an erroneous error I believe.
I have found that, in this case, W= F * d * amount of force delivered, determined by the angle at which the do-er does work to displace.
So, because I have to take into account the hindrance of water to the boat's positive work, do I have to supply this hindrance as a negative energy (in joules) to the positive work being done? In other words, Do I deduct the water's exertion from that of the boat's? or do I add these two energies together and treat on or the other as a positive or negative value?
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