STRATEGY Assuming that friction is negligible compared to other energies, we can
ID: 2078521 • Letter: S
Question
STRATEGY Assuming that friction is negligible compared to other energies, we can use conservation of energy between the top and the bottom of the incline. The potential energy at an elevation h with respect to the bottom is Mgh. The kinetic energy is ½ MV2, regardless of location. It only depends on the speed and the mass The elastic energy stored in a spring, compressed ar distance X from the uncompressed state is ½ kx2 . As the energies change form, we equate energy gains to energy losses since the energy total cannot change in absence of energy dissipative (non-conservative orm the uncompresseinst compressed a As 4:60 kg Mcr26 600 kg M-pers h=25m Mpwnors-600 kg 600 kg k=36 kN/m mx? x,print = ? forces such as friction. IMPLEMENTATION Between the 25-m elevation h and the bottom of the hill, the potential energy loss is equal to Mgh and the kinetic energy gain is equal to ½ M1,2, where h = 25 m and M = 1200 kg. We set AUgwy-AK and find vmap Between the time that the car touches the spring and comes to a complete stop, it loses all of its kinetic energy The energy is absorbed by the compressed spring, which gains an elastic (spring potential energy of ½ kx2 We set AK = 1,ring and solve for the spring compression xqng.Explanation / Answer
1
initial potential energy=mgh,initial kinetic energy=0 as velocity at top=0 m/s
after coming down
potential energy=0 ,kinetic energy=0.5mv^2
conserving energy
mgh=0.5mv^2
we got
v^2=2gh=490
we got v=22.14 m/s
(2) again conserving energy between kinetic energy and elastic energy of spring.As this kinetic energy will be stored as elastic potential energy of spring of the spring
0.5mv^2=0.5*k*x^2
we got
x^2=mv^2/k=16.33
x=4.04 m
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