Frictional Force vs normal force

[Dalip Saini]

Homework Statement

A 10 N horizontal force is applied to a 50 N block initially at rest on a rough horizontal surface. If the coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.4, then the frictional force on the block is

• A
  
  10 N
• B
  
  20 N
• C
• 0 N
• 
  
• 
  
• D
• 
  25 N

Homework Equations

Frictional force = (coefficient of static friction)(normal force)
Normal Force = mass x gravity = 50 N due to Newtons second law

The Attempt at a Solution

Frictional force = 50 * 0.4 = 20 N but the answer is 10 N and I don't understand why

 

[Chestermiller]

With regard to static friction, the frictional force is not always equal to the coefficient of static friction times the normal force. If the frictional force does not exceed (coefficient of static friction)(normal force), then the object will not slide on the surface. In your case it doesn't, so no sliding will occur, and the body will be in static equilibrium, with the frictional force being in equilibrium with the 10 N applied force. In general, for static friction,

(frictional force) ≤ (coefficient of friction)(normal force)Chet

 

[Dalip Saini]

With regard to static friction, the frictional force is not always equal to the coefficient of static friction times the normal force. If the frictional force does not exceed (coefficient of static friction)(normal force), then the object will not slide on the surface. In your case it doesn't, so no sliding will occur, and the body will be in static equilibrium, with the frictional force being in equilibrium with the 10 N applied force. In general, for static friction,

(frictional force) ≤ (coefficient of friction)(normal force)Chet

okay thank you so much