Question

The truck begins stopped at a red light on a state highway. While stopped, the block hangs straight down to a distance 43 cm below the book that attaches th (a) What is the effective spring constant of the cord? (b) What is the Young's modulus of the cord? After the light turns green, the truck begins to accelerate. As it does, the spring stretches to a length 50 cm (c) What is the magnitude of the force on the block? The bungee cord stretches at an angle (the stretching is in the same direction as the cord, Itself). The stretching can be broken down into components. (d) How much does the cord stretch in the 2-direction? (e) What is the direction of the cord form the block to the hook? 9 + (1) What is the accleration of the truck? (9) What is the position of the block with the hook as the origin? 19+ (h) When the truck reaches its cruising speed of 21.2 m/s, what is the position of the opposite end of the bungee cord with respect to the origin? 19 Submit Answer

Answer 1

a) Using F = mg = kx,

k = mg/(SI) = 4.7 * 9.8/(0.43 -0.35) = 575.75N/m

b) The young's modulus is given by

Y = = (4.7* 9.8* 0.35)/(4 * 10-5 * 0.08) = 5037812.5N/m?

c) Using the first equation,

F=k(Sr) = 575.75 * (0.5 -0.35) = 86.3625N

d) The only downward force acting on the body is gravity. So, the downward stretching will be same as before.

dx = 43-35 = 8 cm.

e) Since the present length of string is 0.5 m and the z distance is 0.43 m. the y distance can be found using Pythagoras theorem

y = V0.52 - 0.432 = 0.255m

So,

ā= (0.255ý +0.432)m

f) The displacement in the y direction is 0.255 m.

Using ma = kx,

a = 575.75 * 0.255/4.7 = 31.2375m/s2

g) The position of block with the hook as the origin is same as the vector a.

ā= (0.255ý +0.432)m

h) When the truck is cruising, the acceleration of the truck has stopped and only the gravitational force is present. This is equivalent to the truck at rest.

So,

ā= (Oy + 0.432) m