4. A force of 48 N is required to start a 7.8 kg box moving across a horizontal concrete floor.
(a) What is the coefficient of static friction between the box and the floor?
=
(b) Does the coefficent of friction have a unit?
A. No, it is a ratio
B. No, the units are not real
C. Yes, it is measured in kilograms
D. No, it is just a simple number
E. Yes, it is measured in radians
F. Yes, it is measured in meters
G. No, there are no units of measure
H. Yes, it is measured in Newtons
(c) If the 48 N force continues, the box accelerates at 8.9 m/s^2. What is the coefficient of kinetic friction?
=
a. Wt.of box=m*g=7.8kg * 9.8N/kg=76.44 N
=Fn=Normal force or force perpendicular
to the floor.
Fs = u*Fn = u*76.44 N.=Force of static friction.
Fap-Fs = m*a
48 - u*76.44 = m*0 = 0
u*76.44 = 48
u=0.628 = Coefficient of static friction
b. A. No, it is a ratio. u = Fs/Fn
c. Fap-Fk = m*a
48 - Fk = 7.8*0.89 = 6.942
Fk = 48-6.942 = 41.06 N, = Force of kinetic friction.
u = Fk/Fn = 41.06/76.44 = 0.537
(a) To find the coefficient of static friction between the box and the floor, we can use the equation:
Coefficient of static friction = Force required to start the object moving / Normal force
In this case, the force required to start the box moving is given as 48 N. The normal force can be calculated using the equation:
Normal force = mass * gravity
where mass is 7.8 kg and gravity is approximately 9.8 m/s^2. Therefore, the normal force is:
Normal force = 7.8 kg * 9.8 m/s^2 = 76.44 N
Now we can substitute the values into the first equation to find the coefficient of static friction:
Coefficient of static friction = 48 N / 76.44 N = 0.628
So, the coefficient of static friction between the box and the floor is approximately 0.628.
(b) The correct answer is G. No, there are no units of measure. The coefficient of friction is a dimensionless quantity, defined as the ratio of the force of friction to the normal force.
(c) To find the coefficient of kinetic friction, we can use the equation:
Coefficient of kinetic friction = Force of kinetic friction / Normal force
From the equation of motion, we know that force of kinetic friction is equal to mass * acceleration:
Force of kinetic friction = mass * acceleration
= 7.8 kg * 8.9 m/s^2
= 69.42 N
We already calculated the normal force in part (a) as 76.44 N. Substituting the values into the equation for the coefficient of kinetic friction:
Coefficient of kinetic friction = 69.42 N / 76.44 N = 0.908
So, the coefficient of kinetic friction between the box and the floor is approximately 0.908.