Answer to Question #214176 in Physics for ...

Question

The coefficient of static friction between a 20-kg block and a horizontal surface is 0.25 

and the coefficient of kinetic friction is 0.15. A cord is attached to the block, the cord 

making an angle of 10 degrees with the horizontal. (a) What tension in the cord will just 

start the block? (b) What is the tension in the cord when the block moves with uniform 

velocity?

Answer 1

(a)

$$F_Tcos\theta-F_{s.fr}=0,$$ $$F_Tcos\theta-\mu_smg=0,$$ $$F_T=\dfrac{\mu_smg}{cos\theta}=\dfrac{0.25\cdot20\ kg\cdot9.8\ \dfrac{m}{s^2}}{cos10^{\circ}}=49.75\ N.$$

(b) Since the block moves with uniform velocity, the acceleration is equal to zero:

$$F_Tcos\theta-F_{k.fr}=0,$$ $$F_Tcos\theta-\mu_kmg=0,$$ $$F_T=\dfrac{\mu_kmg}{cos\theta}=\dfrac{0.15\cdot20\ kg\cdot9.8\ \dfrac{m}{s^2}}{cos10^{\circ}}=29.85\ N.$$