A block with mass m1 = 8.6 kg is on an incline with

an angle ? = 32� with respect to the horizontal. For the first

question there is no friction between the incline and the

block.

1) When there is

no friction, what is the magnitude of the acceleration of the

block?

2) Now with

friction, the acceleration is measured to be only a = 3.95

m/s2. What is the coefficient of

kinetic friction between the incline and the block?

3)

To keep the mass from accelerating, a spring is attached with

spring constant k = 168 N/m. What is the coefficient of static

friction if the spring must extend at least x = 14 cm from its

unstretched length to keep the block from moving down the

plane?

4)

The spring is replaced with a massless rope that pulls

horizontally to prevent the block from moving. What is the tension

in the rope?

5)

Now a new block is attached to the first block. The new block is

made of a different material and has a coefficient of static

friction ? = 0.94. What minimum mass is needed to keep the system

from accelerating?

1 ) a =gsintheta = 5.193 m/s^2

2) a = gsintheta -u*gcostheta

3.95 = 9.8*(sin32 -u*cos32)

u =coeficient = 0.149

3)

k*x = mgsintheta - mu*gcoatheta

168*0.14 = 8.6*9.8*(sin32 - ucos32 )

u = 0.295

4)

we get u =coeficent = 2.205

g*m sin 32 = T cos32 [2.205*( Tsin32 mgcos32) ]

44.66 = Tcos32 0.295*Tsin32 21.08

23.52 = T*(0.848 0.156 )

T =tension = 23.426 N

5)

let mass required be m then we get equations as follows

8.6*9.8*sin32 - 8.6*9.8*0.295*cos32 = T

T = 23.576 N

now

T m*9.8*sin32 = 0.94*m*9.8*cos 32

23.576 5.19m = 7.81m

m = 8.998 kg