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?
\mu_s =
(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 \frac{m}{s^2}. What is the coefficient of kinetic friction?
\mu_k =
Hey, all of these are basically the same question. If you want to pass the course you better learn how to do one of them.
To find the coefficient of static friction between the box and the floor, we can use the equation:
\( f_{\text{{max}}} = \mu_s \cdot N \)
where \( f_{\text{{max}}} \) is the maximum force of static friction, \( \mu_s \) is the coefficient of static friction, and \( N \) is the normal force. In this case, since the box is on a horizontal surface, the normal force is equal to the box's weight, which can be calculated as:
\( N = m \cdot g \)
where \( m \) is the mass of the box and \( g \) is the acceleration due to gravity (approximately 9.8 m/s\(^2\)).
(a) Calculating the maximum force of static friction:
\( f_{\text{{max}}} = 48 \, \text{{N}} \)
\( m = 7.8 \, \text{{kg}} \)
\( g = 9.8 \, \text{{m/s}}^2 \)
Using the formula for the normal force, \( N = m \cdot g \), we can find N:
\( N = 7.8 \, \text{{kg}} \cdot 9.8 \, \text{{m/s}}^2 \)
Now, we can substitute the value of N into the equation for the maximum force of static friction:
\( 48 \, \text{{N}} = \mu_s \cdot (7.8 \, \text{{kg}} \cdot 9.8 \, \text{{m/s}}^2) \)
To solve for \( \mu_s \):
\( \mu_s = \frac{{48 \, \text{{N}}}}{{(7.8 \, \text{{kg}} \cdot 9.8 \, \text{{m/s}}^2)}} \)
Simplifying the expression will give us the coefficient of static friction.
(b) The coefficient of friction is a ratio and, therefore, does not have any units. Thus, the answer is G. No, there are no units of measure.
(c) To find the coefficient of kinetic friction, we can use the equation:
\( f_k = \mu_k \cdot N \)
where \( f_k \) is the force of kinetic friction. In this case, since the box is accelerating, the force of kinetic friction can be calculated as:
\( f_k = m \cdot a \)
where \( m \) is the mass of the box and \( a \) is the acceleration of the box.
Using the formula for the normal force, \( N = m \cdot g \), we can substitute the value of \( N \) and \( f_k \) into the equation above:
\( m \cdot a = \mu_k \cdot (m \cdot g) \)
Simplifying the expression will give us the coefficient of kinetic friction.