Question

What is the answer for a,b,c and d?A 1.20-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of v, = 3.40 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distanced (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e).(a) Find the distance of compression d (in m). (b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). m/s (c) Find the distance D (in m) where the object comes to rest. m (d) What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving

Answer 1

Given that the mass of the object is m = 1.2 kg

The coefficient of kinetic friction is given as

`\mu_k=0.25`

The speed of the object is

`v_i=\text{ 3.4 m/s}`

The force constant is

`k=\text{ 50 N/m}`

We have to find the compression, d.

According to the conservation of energy

`-(1)/(2)kd^2+(1)/(2)m(v_i)^2-\mu_kmgd=0`

Here, g = 9.8 m/s^2 is the acceleration due to gravity.

Substituting the values, the compression will be

`\begin{gathered} -(1)/(2)*50* d^2+(1)/(2)*1.2*(3.4)^2-0.25*1.2*9.8* d \\ -25d^2+6.936-2.94\text{d=0} \\ d=\text{ }0.471\text{ m} \end{gathered}`