Question

A block of mass 2 kg that sits on a horizontal table is connected to a block of mass 6 kg that sits on a ramp of angle 34 ⁰down from the horizontal by a massless string that runs over a pulley in the shape of a solid disk having radius 0.93 m and mass 10 kg. The coefficient of friction for both blocks is 0.256.

(a) What is the acceleration of the blocks?


(b) The tension in the string connected to the horizontal block.


(c) The tension in the string connected to the block on the ramp.

Answer 1

here,

mass of block on horizontal , m1 = 2 kg

mass of block on ramp , m2 = 6 kg

theta = 34 degree

radius , r = 0.93 m

mass of pulley , m = 10 kg

u= 0.256
a)

the accelration of the blocks , a = net force/effective mass

a = ( m2 * g * sin(theta) - u * m2 * g * cos(theta) - u * m1 * g )/(m1 + m2)

a = ( 6 * 9.81 * sin(34) - 0.256 * 9.81 (6 * cos(34) + 2 )) /(2 + 6) m/s^2

a = 1.92 m/s^2

b)

let The tension in the string connected to the horizontal block be Th

for m1

Th - u * m1 * g = m1 * a

Th = 2 * ( 1.92 + 0.256 * 9.81) N

Th = 8.86 N

c)

let The tension in the string connected to the block on the ramp be Ti

m2 * g * sin(theta) - Ti - u * m2 * g * cos(theta) = m2 * a

Ti = 6 * ( 9.81 * sin(34) - 0.256 * 9.81 * cos(34) - 1.92) N

Ti = 8.9 N