Answer to Question #253288 in Mechanics | Relativity for lakhte

Question

Use the following information to answer the next two independent questions.

A block of mass 5.4

5.4 kg is situated on the incline as shown. It is attached to an anchored spring of stiffness 136

136 N/m, also as shown.

The incline angle is such that sin(𝜃)=4/5,cos(𝜃)=3/5

sin⁡(θ)=4/5,cos⁡(θ)=3/5. Take g = 9.81 m/s² and enter both answers correct to three sig digs.

a) [2] If the spring is stretched by 0.3

0.3 m, and the block remains at rest then what is the magnitude and direction of the static frictional force acting on the block?

(With x-positive measured down the incline, enter a positive value if your static friction points down the incline, and a negative value if it points up the incline.)

𝑓𝑠=?

b) [2] If the coefficient of static friction is 0.53

0.53, what is the largest extension the spring can have from its equilibrium length so that the block remains motionless?

𝑥𝑚𝑎𝑥=?

Answer 1

a)

$mgsin\theta-kx-f_{s}=0$

$f_s=mgsin\theta-kx=5.4\cdot 9.81\cdot 4/5-136\cdot0.3=1.58$ N

b)

$x=\frac{mgsin\theta -f_s}{k}$

$f_s=\mu N=\mu mgcos\theta$

where $\mu$ is the coefficient of static friction.

$x=\frac{mgsin\theta -\mu mgcos\theta}{k}=\frac{5.4\cdot 9.81\cdot 4/5-0.53\cdot 5.4\cdot 9.81\cdot 3/5}{136}=0.19$ m