C) Calculate the coefficient of kinetic friction between the box and the ramp. 1

Question

C) Calculate the coefficient of kinetic friction between the box and the ramp. 19. (15 pts) A 3.0-kg block is resting on a table is attached to a 1.0 kg by a light string as shown (ignore the friction of the pulley). The coefficient of static friction between the table and the 3.0-kg block is 0.40. A) What is the static of friction between the table and the r block? If the 1.0kg mass is replaced by a 2.0-kg, the system begins to fi 11 accelerate from rest. The coefficient of kinetic friction between the block and the table is 0.3 0. B) Find tension T in the string. C) What is the acceleration of 3.0 kg and 2.0 kg mass?

Explanation / Answer

minimum force required to move the block = mg* mu = 3*9.8* 0.4 = 11.76 N,

now, ,
Tension pulling the block,

T = 1*9.8 = 9.8 N
, so as T is less than minimum force required to move the block

so,
friction will work , but exactly equal to tension acting to nullify its effect,

so ,

friction = 9.8 N

B) now ,
if the block is of 2 kg and given the block is moving , hence ,max friction will act to minimise the motion,
i.e ,f = 11.76 N
so ,

writing the equation of motion,
T- f = 3a

and

2*g-T = 2a

putting values,
T - 11.76 = 3a.............(1)

2*9.8-T = 2a..........(2)

solving these two,

a= (19.6-11.76)/5
a= 1.568 m/s^2

C) T = 3*1.568+11.76

T = 16.464 N

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