A cart full of Tomato soup is moving through the factory area( mass of soup and
ID: 1375812 • Letter: A
Question
A cart full of Tomato soup is moving through the factory area( mass of soup and cart M=200 kg). at the top of the first hill, at point A, the speed is 10m/s. the cart is to stop at ground level and the safety engineering is considering stopping the cart in one TWO WAYs: first, the cart can apply its breaks and slide to a stop( uk=0.4).
Second, the cart can run into a big agiant spring( k=4,000 N/m)
A)Show that the total initial energy of the soup and the cart is 402,00 J.
B) Show that if the first method of stopping is used, that the cart will slide a distance of 513m ( half of a kilometer)
C) Show that if the second method of stopping is used, that the spring is compressed a distance of 14.2 m
D) What is a major safety issue related to a person riding in the cart in place of the soup if they use the second method of stopping the cart?
A cart full of Tomato soup is moving through the factory area( mass of soup and cart M=200 kg). at the top of the first hill, at point A, the speed is 10m/s. the cart is to stop at ground level and the safety engineering is considering stopping the cart in one TWO WAYs: first, the cart can apply its breaks and slide to a stop( uk=0.4). Second, the cart can run into a big agiant spring( k=4,000 N/m) A)Show that the total initial energy of the soup and the cart is 402,00 J. B) Show that if the first method of stopping is used, that the cart will slide a distance of 513m ( half of a kilometer) C) Show that if the second method of stopping is used, that the spring is compressed a distance of 14.2 m D) What is a major safety issue related to a person riding in the cart in place of the soup if they use the second method of stopping the cart?Explanation / Answer
A) Intila mechanical enrgy = 0.5*M*v^2 + M*g*H
= 0.5*200*10^2 + 200*9.8*200
= 402000 J
B) workdone by friction = change in mechanica enrgy
F*d*cos(180) = -402000
mue_k*m*g*d*(-1) = -402000
0.4*200*9.8*d = 402000
d = 402000/(0.4*200*9.8)
= 512.76 m
c) Apply ENrgy coservation
final elastic potentail enrgy = initial mechanical enrgy
0.5*k*x^2 = 402000
x = sqrt(2*402000/4000)
= 14.18 m
d) The negative acceleration is too large which a human being can not bear.
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