## A spring gun with a 75 N/m spring constant is loaded with a 5 g foam dart and isaimed vertically. When the spring is compressed by 10 cm and

Question

A spring gun with a 75 N/m spring constant is loaded with a 5 g foam dart and isaimed vertically. When the spring is compressed by 10 cm and then released, the fireddart rises to a max height of 5 m above the end of the spring gun. Assuming the dartexperiences a constant friction force due to the air, how fast is it traveling when ithas fallen 2 m from its maximum height

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6 months 2021-07-17T21:08:50+00:00 1 Answers 7 views 0

The speed is

Explanation:

From the question we are told that

The spring constant is

The mass of the foam dart is

The compression distance is

The height which the gun raised the dart is

The change in height is

The new height is

Generally from the law of conservation of energy

Where is the energy stored in spring and it is mathematically represented as

KE is the kinetic energy possessed by the dart when it is being shut and this is mathematically represented as

So

Substituting values

=>

When the dart is at  the maximum height the

let it acceleration due air resistance be z

So by equation of motion

Where v is the velocity at maximum height which is equal to zero

and  u is it initial velocity before reaching maximum height which we calculated as

and a is the acceleration due to gravity + the acceleration due to air resistance

So

a =  z+g

=  9.8 + z

=>

Substituting values

Making z the subject

When the dart is moving downward we can mathematically represent the motion as

Since the motion is downward and air resistance is upward we have that

a =  g – z

and the the initial velocity u becomes the velocity at maximum height

i.e u = 0

And v is the velocity the dart has when it is moving downward

So

Substituting values