a)A uniform chain has mass m = 5.86 kg and length L = 7.45 m. It is held on a fr

Question

a)A uniform chain has mass m = 5.86 kg and length L = 7.45 m. It is held on a frictionless table with L/11 hanging over the edge. Find the work needed to pull the hanging part back onto the table.
NOTE: There is an easy way and an hard way to do this problem!

b)A one-dimensional force acts on a particle of mass m = 2.06 kg in such a way that its position is given by:

Find W, the work done by this force during the first 4.95 s.

c) Suppose the magnitude of the force needed to tow a boat at constant velocity is directly proportional to its speed:

If it takes P1 = 4.65 kW to tow the boat at constant speed v1 = 4.76 m/s, find P2, the power would it take to tow the boat at constant speed v2 = 7.8 m/s.

d)A one-dimensional potential is given by: U(x) = -2.88x3 + 8.66x + 3.84 where U is in Joules when x is in meters. Find the magnitude of the force associated with this potential when x = 3.74 m.

Explanation / Answer

a)W=(change of potential energy) =( m/l * l/11 ) * g* (l/11*1/2) [ cm of hanging part at l/11*1/2 from the table] =1.77 J c)P=int F.dv=kv^2/2 so P2/P1=(v2/v1)^2 so P2=P1*7.8^2/4.76^2=12.5 W d)U(x) = -2.88x3 + 8.66x + 3.84 so du/dx=-F=-8.64 x^2 + 8.66 so F(3.74)=112.2

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