Question

7) A 2.50-kg block is on a 53.0⁰ incline for which coefficient of kinetic friction = 0.25 and coefficient of static friction = 0.50. Find its acceleration given that: (a) it is initially at rest; (b) it is moving the slope; (c) it is moving down the slope.

Answer 1

7)

a)

When the block is at rest and not moving, the acceleration of the block is 0 m/s² Since the sum of all the forces comes out to be zero.

b)

F_n = normal force on the block by the incline surface

= Angle of the incline = 53 deg

= Coefficient of kinetic friction = 0.25

From the force diagram , force equation perpendicular to incline surface is given as

F_n = mg Cos

Kinetic frictional force is given as

f_k = F_n

f_k = mg Cos

parallel to incline surface, force equation is given as

- mgSin - f_k = ma

- mgSin - mg Cos = ma

a = - gSin - g Cos

a = - (9.8)Sin53 - (0.25 x 9.8)Cos53

a = - 9.301 m/s²

The negative sign indicates acceleration is in down direction parallel to incline surface

c)

F_n = normal force on the block by the incline surface

= Angle of the incline = 53 deg

= Coefficient of kinetic friction = 0.25

From the force diagram , force equation perpendicular to incline surface is given as

F_n = mg Cos

Kinetic frictional force is given as

f_k = F_n

f_k = mg Cos

parallel to incline surface, force equation is given as

- mgSin + f_k = ma

- mgSin + mg Cos = ma

a = - gSin + g Cos

a = - (9.8)Sin53 + (0.25 x 9.8)Cos53

a = - 6.35 m/s²

The negative sign indicates acceleration is in down direction parallel to incline surface