1/ A block of mass m = 1.8 kg is dropped from height h = 41 cm onto a spring of
ID: 1768065 • Letter: 1
Question
1/ A block of mass m = 1.8 kg is dropped from height h = 41 cm onto a spring of spring constant k = 2470 N/m (see the figure). Find the maximum distance the spring is compressed.
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2/ Tarzan, who weighs 669 N, swings from a cliff at the end of a convenient vine that is 15 m long (see the figure). From the top of the cliff to the bottom of the swing, he descends by 2.2 m. The vine will break if the force on it exceeds 1220 N. What would the greatest force on the vine be during the swing?
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3/ The boy in the figure here is initially seated on the top of a hemispherical ice mound of radius R = 13.9 m. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At what height does the boy lose contact with the ice?
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4/A single conservative force F(x) acts on a 4.3 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by
U(x) = -2.4xe-x/3
where x is in meters. At x = 1.1 m the particle has a kinetic energy of 2.7 J. (a) What is the mechanical energy of the system? (b) What is the maximum kinetic energy of the particle and (c) the value of x at which it occurs?
Explanation / Answer
1) m*g*(h+x) = 0.5*k*x^2
1.8*9.8*(0.41+x) = 0.5*2470*x^2
7.2324 + 17.64*x = 1235*x^2
1235*x^2 - 17.64*x - 7.2324 = 0
solving the above equation we get
x = 0.084 m
= 8.4 cm
2) at lowest point, v = sqrt(2*g*h_ = sqrt(2*9.8*2.2) = 6.57 m/s
Tmax = M*g + M*v^2/r
= 669 + (669/9.8)*6.57^2/15
= 865.24 N
3)
4)
a) TE = U + K
= -2.4*e^(-1.1/3) + 2.7
= +0.98 J
b) when U is minimum KE becomes maximium
when U is minium, dU/dx = 0
-2.4*e^(-x/3)*(-1/3) = 0
==> x = 0
when x = 0, U = -2.4 J
we know, TE = Umin + KEmax
KEmax = TE - Umin
= 0.98 - (-2.4)
= 3.38 J
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