Help?please

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2 Answers
Jul 16, 2017

0.191131498.....

Explanation:

For the purpose of simplicity let the acceleration due to the gravity near the earth's surface be g = 9.81m/s^2

To find the initial speed with which the object is launched at the INSTANT it leaves the spring,
k = 200 N/m
1/2 kx^2 = 1/2 mv_0^2 where k is the spring constant of the spring

cancelling the 1/2on either side and rewriting to solve for v, we get v_0 = sqrt((kx^2) / m)
v_0 = sqrt((200*(0.15)^2)/2)
v_0 = sqrt(2.25) = 1.5 m/s

The general formula for Work is W = Force * distance = F * d
To find work done by friction, since it opposes the direction of motion of the block,
W_f = -mu_k*F*d = -mu_k*m*g*d

Since the block comes to rest and all the kinetic energy is converted to heat due to friction and other forms of energy,
-mu_k*m*g*d = -1/2mv_0^2

Rewriting to solve for mu_k gives us
mu_k = v_0^2/(2*g*d)
mu_k = (1.5)^2/(2*9.81*0.6) = 2.25/11.772 ~~ 0.191131498... ~~0.191

Therefore mu_k ~~ 0.191

Jul 16, 2017

0.19, two significant figures

Explanation:

As the spring is compressed it has mechanical potential energy which is given by the expression

PE=1/2 kx^2
where k is spring constant and x is deformation of the spring.

On releasing of spring, all this energy is transferred to the block as its kinetic energy.

As the block moves on the horizontal surface, its kinetic energy is used to do work against force of friction vecF

Now vecF=mu_kvecN
where mu_k is coefficient of friction and vec N is normal reaction=mvecg.

Inserting various values we have
F=mu_kxx2.0xx9.8=19.6mu_k

We know that work done is W = vecF * vecs

In this case theta angle between the force of friction and displacement is 0^@=>cos theta=cos0^@=1.

:.W = F * s
=>W = 19.6mu_k xx 0.60

Since the block comes to rest this is equal to initial potential energy of the spring. Equating the two we get

19.6mu_k xx 0.60=1/2kx^2

Inserting given values we get
19.6mu_k xx 0.60=1/2xx200xx (0.15)^2
=>mu_k =100xx (0.15)^2xx1/(19.6xx0.60)
=>mu_k = 0.19, two significant figures