A Hooke\'s law spring is compressed a distance d and is used to launch a mass m

Question

A Hooke's law spring is compressed a distance d and is used to launch a mass m vertically to a height h above its starting position. Under double the the spring is now used to launch the mass. How high does the mass now rise above its starting position? O b. 3h d. 4h QUESTION 7 A bank vault is opened by applying a force of 140 N perpendicular to the plane of the door, 1,20 m from the hinges. Find the torque due to this force about an axis through the hinges. O a. 308 N m Ob. 117N·m O c. 140 N-m O d. 154 N-m O e. 168 N m QUESTION 8 Petra pushes a crate across a rough floor. A frictional force of 28.0 N acts to oppose the motion of the crate, and Petra pushes with a horizontal force of 364N. If the net work Petra does is 94.5 J, through what distance did she push the crate? O a. 3.38 m o b. 2 650 nm O d. 2.60 m e. 3 440 m Click Save and Submit to save and submit. Click Save All Answers to save all ansuers MacBook Air

Explanation / Answer

Question 6:

hooke’s law states that, spring force=-k*x

where k=spring constant

x=compression distance

initial potential energy stored in a spring =0.5*k*x^2

this energy is converted to gravitational potential energy when it reaches maximum height h.

using energy conservation principle,

0.5*k*x^2=m*g*h

==>h=0.5*k*x^2/(m*g)

so when compression is x=d, height is h.

when compression doubles to 2*d, height becomes 2^2=4 times

hence option D is correct.

Question 7:

torque=force*perpendicular distance

=140*1.2

=168 N

hence option E is correct.

question 8:

net work done by petra=net force applied*distance

==>94.5=(36.4-28)*distance

==>distance=11.25 m

hence option C is correct answer.

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