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(solution) I would like to get some in depth help on how to do all problems


I would like to get some in depth help on how to do all problems and parts to each problem. Solving each part with steps.


Name: Section: Open Response Homework 16: Work

 

Problem 1 An object with inertia m = 2 kg is connected to a spring with spring constant k = 400 N/m and

 

equilibrium position at x0 = 7 cm (for x > x0 , the force is directed toward the origin). The object is initially

 

at rest at position x = 14 cm. You grab the object and move it slowly to position x = 28 cm. After you finish

 

moving it, you continue to hold the object at rest at its new position.

 

(a)[6 pts] What is the potential energy stored in this process? Assume the system is the object and the

 

spring.

 

(b)[5 pts] How much work did you do on the object?

 

Problem 2 A cat toy consists of a long spring with a fake mouse of some inertia m attached to one end. The

 

other end is attached to the ceiling. The mouse is initially at rest. A cat pulls the mouse down, holds it at rest

 

for a moment, and releases it. Consider the motion of the mouse from the time the cat releases it, until it returns

 

to its equilibrium position, and take the mouse alone to be your system. Neglect the inertia of the spring.

 

(a)[6 pts] What forces act on the mouse, in what directions? Are the forces constant?

 

(b)[7 pts] Considering the mouse alone as your system, what is the work done on it?

 

Problem 3 Two identical 4kg carts on a very long table of negligible friction are connected by a relaxed horizontal

 

N

 

. You pull one cart with some constant horizontal force. After a time, the

 

spring with spring constant 240 m

 

separation between the carts remains constant and the spring is stretched by 0.1m. For part (a) you are solving

 

for some time after the spring has achieved a constant stretch.

 

(a)[7 pts] What pulling force did you apply to the cart to reach this constant stretch?

 

(b)[9 pts] Now, let?s think about as the carts first started moving, but before the spring reached the constant

 

stretch. Before they started to move (spring relaxed) they were 20cm apart. Call the location of the block

 

you are not directly pulling 0 at the start. At some instant after you started pulling with the constant

 

force you found above (time t1 ), imagine that the block you were pulling had moved 4cm (it is now at

 

x = 24cm) and the following block had moved 2cm, to x = 2cm.

 

?Where was the center of mass of the two identical blocks before they started to move?

 

?How far has the center of mass moved from the time you started until t1 ?

 

?How far has the point of application of the force moved in this time?

 

?What is the work done on the system by the pull?

 

?What is the translational kinetic energy of the system?

 

?Why are these two numbers different (if they are)?

 

Problem 4 A new construction crane has the following specifications: The hook has mass 1000kg, the maximum

 

capacity of the hook is 400kg, the constant lifting speed of the hook is 1.5 ms , and the hook must achieve this

 

speed in 2 seconds at a constant acceleration, beginning at rest.

 

(a)[7 pts] What is the maximum average power the crane motor must deliver to get up to cruising speed?

 

(b)[5 pts] What constant power must the motor supply as the hook rises, after attaining its cruising speed

 

upward?

 

Problem 5 1 A very large dog, a 60kg Great Dane, is jumping up to grab a

 

snack held off the edge of a deck by his master, 3.2m above the

 

ground. The 1m tall dog can crouch down until his center of mass

 

is 0.3m above the ground. When his feet leave the ground (he can

 

no longer push), his center of mass is 0.8m off the ground. He

 

can push against the ground with a force 4 times the magnitude

 

of his own weight. (a) dog (a)[5 pts] If you were to identify just the dog as your system,

 

find the value of the net external force on the dog as he

 

is pushing off the ground.

 

Make sure to draw a free body diagram on the figure to

 

the right for the dog during this time (while his feet are

 

in contact with the ground). (c) (b)[2 pts] What objects would you need to draw to include

 

the force pairs of the forces drawn on the dog?

 

(c)[4 pts] Assuming the dog was at rest when it started

 

pushing, what is its kinetic energy when its feet leave the

 

ground? 0 (d)[8 pts] How much work did the ground do on the dog

 

(write this down!)?

 

Carefully draw a work-energy diagram on the figure to

 

the right showing how energy was transferred during the

 

push for the defined system (the dog). Assume the dog?s

 

muscles are not perfectly efficient.

 

(e)[5 pts] Does the dog grab the treat? Assume he gets the

 

treat if his center of mass reaches 3m above the ground.

 

(f)[5 pts] What is the impulse delivered to the dog by the

 

ground when he lands? 2 K U Ediss Esource Work

 


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