Does Friction Affect the Acceleration of a Sliding Block?

[inkandgold]

Homework Statement

The coefficient of static friction between a block and a horizontal floor is 0.44, while the coefficient of kinetic friction is 0.10. The mass of the block is 5.4 kg and it is initially at rest.

(a) What is the minimum horizontal applied force required to make the block start to slide?
(b) Once the block is sliding, if you keep pushing on it with the same minimum starting force as in part (a), does the block move with constant velocity or does it accelerate?
(c) If it moves with constant velocity, what is its velocity (in m/s)? If it accelerates, what is its acceleration (in m/s2)?

Homework Equations

F = ma
f_s = u_sN

The Attempt at a Solution

a) F=ma
F=(5.4kg)(9.8m/s/s) = 52.92, which isn't right

b) I believe it will accelerate.

c) It's not 9.8 m/s/s. I will probably have to find it via F=ma?

Thanks so much for your help!

 

[inkandgold]

Well, I figured out part a! a = 5.4 kg * 9.8m/s/s *.44 = 23.3. Still unsure about the rest though.

 

[PhanthomJay]

Well, I figured out part a! a = 5.4 kg * 9.8m/s/s *.44 = 23.3. Still unsure about the rest though.

You can answer the rest by using Newton's 2nd Law, F_net = ma, where F_net is the algebraic sum of the applied force and the friction force. Watch plus/minus signs.

 

[inkandgold]

Thanks so much, got it now!

 

[rwisz]

I would first clarify the homework statement by asking for the specific units of the coefficients of friction (static and kinetic) and the mass of the block. I would also ask for the direction of the applied force, as it can affect the calculations. Assuming that the units are in SI (meters, kilograms, seconds), the mass of the block is 5.4 kg, and the force is applied horizontally, I would approach the problem as follows:

(a) The minimum horizontal force required to make the block start to slide can be calculated using the equation F = μsN, where μs is the coefficient of static friction and N is the normal force exerted by the surface on the block. Since the block is initially at rest, the normal force is equal to the weight of the block, which is given by mg, where g is the acceleration due to gravity (9.8 m/s^2). Therefore, the minimum force required to make the block start to slide is:

F = μsmg = (0.44)(5.4 kg)(9.8 m/s^2) = 23.83 N

(b) Once the block is sliding, the kinetic friction force will be in effect, and it will oppose the motion of the block. This means that the applied force must be greater than the kinetic friction force in order for the block to continue moving with constant velocity. Therefore, the block will accelerate if the applied force remains constant.

(c) If the block accelerates, its acceleration can be calculated using the equation F = ma, where F is the net force acting on the block. The net force is equal to the applied force minus the kinetic friction force, so:

F = ma
F - μkmg = ma
(a - μkmg) = ma
a = (a - μkmg)/m
a = (23.83 N - (0.1)(5.4 kg)(9.8 m/s^2))/5.4 kg = 3.48 m/s^2

If the block moves with constant velocity, its velocity can be calculated using the equation F = ma, where F is the net force acting on the block. Since the net force must be equal to the applied force (to counteract the kinetic friction force), the velocity can be calculated as:

F = ma
a = F/m
a = (23.83 N)/5.4 kg