Use the worked example above to help you solve this problem. A 0.481 kg block re

Question

Use the worked example above to help you solve this problem. A 0.481 kg block rests on a horizontal, frictionless surface as shown in the figure. The block is pressed back against a spring having a constant of k = 626 N/m, compressing the spring by 11.5 cm to point . Then the block is released. (a) Find the maximum distance d the block travels up the frictionless incline if = 30.0°. m (b) How fast is the block going when halfway to its maximum height? m/s EXERCISE A 1.32 kg block is shot horizontally from a spring, as in the example above, and travels 0.479 m up a long a frictionless ramp before coming to rest and sliding back down. If the ramp makes an angle of 45.0° with respect to the horizontal, and the spring originally was compressed by 0.11 m, find the spring constant. N/m

Explanation / Answer

1) a)  Approach this from the conservation of energy.
The energy of a compressed spring is (1/2)kx^2
Change in gravitational potential energy is mgh
Kinetic energy is (1/2)mv^2
At any point (1/2)kx^2=mgh+(1/2)mv^2
When the block reaches its maximum height it will have a velocity of zero so,
(1/2)kx^2=mgh =======> h = 0.878 m
Once you get h you must use trigonometry to find how far along the incline it has gone.
h/(distance)=sin(30) =====> distance = 1.76 m

b) h' = h/2 = 0.439 m

then (1/2)kx^2=mgh'+(1/2)mv^2

0.5*626*0.115^2 = 0.481*9.8*0.439 + 0.5*0.481*v^2

v = 2.934 m/s

2) Here 0.5kx^2 = mgL*sin45

k = 1.32*9.8*0.479*sin45/(0.5*0.11^2) = 724.21 N/m

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