the coefficients of static and kinetic friction between a 50.0 kg box and a horizontal surface are 0.500 and?

Question

0.400 respectively. (1) What is the acceleration of the object if a 250-N horizontal force is applied to the box? (2) What is the acceleration if the applied force is 235-N?

Answer 1

the net force of the applied force minus the friction is equal to mass times acceleration

The force only needs to be greater than static friction to get the box moving, then we look at kinetic as the resistive force during motion.

therefore, using 9.81 as g
1. 50*.5*9.81 is less than 250, so the box will move.
While moving
50*a=250-50*.4*9.81

2. Since the static force is 245 N, a 235 N force will not accelerate the box.

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Answer 2

Fnet = mass * acceleration

Fnet is the resultant forces. In this case, Friction and a horizonal force make up Fnet.

Friction = μ( Fnormal )

Static friction force occur when the object is at rest.
Kinetic friction force occurs when the object is in motion

The 250N force is applied when the box is still at rest. Therefor, to find friction, we must use static coefficient of friction

Friction = .5 (50 * 9.8)
Friction = 245N

since Friction is always opposite of the motion, let's make it negative friction force.

250 - 245 = 50a
5 = 50a
a = 0.1 m/s^2

b) Now that the box is moving, the friction between the box and the floor is kinetic friction.

Friction = .4(50*9.8)
Frictio = 196N

235 - 196 = 50a
a = 0.78 m/s^2