A 6kg box is initially moving at 11 m/s to the left. All surfaces are frictionle

Question

A 6kg box is initially moving at 11 m/s to the left. All surfaces are frictionless except the frictional patch just after point B. The box goes over a hill with a radius at the top equal to 5 meters. The box proceeds down the hill into a frictional patch (mu_k = 0.25, d = 4m) and then is stopped by a spring. Answer the following questions in regards to the situation. Sketch a free body diagram for point A indicating relative magnitudes of forces. Calculate the normal force by the hill on the box at point A. Calculate the speed of the block at point B. Calculate the distance the spring is compressed when the box comes to rest.

Explanation / Answer

Toatl energy of mass at extreme right = mgh + 1/2 mv^2 = ( 6x 9.8 x4) + 0.5 ( 6) ( 11)^2= 235. 2 + 363= 598. 2 J

Total energy of mass at A = (6 x 9,8 x 9) + 1/2 mv^2 = 598. 2 J

3v^2 = 69

v= 4.79 m/s apprx

b) Normal force = mg - mv^2/ r = 31. 2 N

c) we can use conservation of energy to calculate the speed at B

598. 2 = 1/2 (6) v^2

v = 14.12 m/s apprx

d) speed of block afer crossing rough patch

v^2 = 14.12^2 - 2 ( 0.25 ) (9.8) (4) = 199.4 - 19.6

v = 13.41 m/s apprx

using conservation of energy

1/2 mv^2 = 1/2 kx^2

6( 13.41 )^2 = 1000 (x)^2

x = 1.038 m apprx

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