ou are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of
F =
+214i − 171k
N
to try and move the 64.0-kg refrigerator. The coefficient of static friction is 0.660.
(a) How much static frictional force does the floor exert on the refrigerator? Express your answer in vector form.
(b) What magnitude of maximum force do you need to apply before the refrigerator starts to move?
(a) Well, well, well, looks like we've got a "static" situation here! To find the static frictional force, we need to first calculate the maximum static frictional force, which can be done using the equation:
f_static max = μ_s * N,
where μ_s is the coefficient of static friction and N is the normal force exerted by the floor on the refrigerator. In this case, since the refrigerator is not moving vertically, the normal force N is equal to its weight, which can be calculated as:
N = m * g,
where m is the mass of the refrigerator (64.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the values, we have:
N = (64.0 kg) * (9.8 m/s^2) = 627.2 N.
Now we can calculate the maximum static frictional force:
f_static max = (0.660) * (627.2 N) = 413.09 N.
Since frictional forces oppose motion, the static frictional force must be equal in magnitude and opposite in direction to the applied force. Thus, the final answer in vector form for the static frictional force is:
f_static = -413.09i + 413.09k N.
(b) Ah, the force needed to bring that stubborn refrigerator to life and make it move! To get that, we'll need to apply a force greater than the maximum static frictional force. So, the magnitude of the maximum force we need to apply is simply the magnitude of the maximum static frictional force:
|f_static max| = |413.09 N| = 413.09 N.
Remember, my friend, apply force with care, but make sure it's a force greater than that maximum static frictional force! Good luck with that refrigerator!
To find the static frictional force exerted by the floor on the refrigerator, we can use the equation:
F_friction = μ_friction * N
Where:
- F_friction is the static frictional force
- μ_friction is the coefficient of static friction
- N is the normal force
In this case, the normal force is equal to the weight of the refrigerator, which can be calculated as:
N = m * g
Where:
- m is the mass of the refrigerator
- g is the acceleration due to gravity
(a) Calculate the normal force:
m = 64.0 kg
g = 9.8 m/s^2
N = (64.0 kg) * (9.8 m/s^2)
N = 627.2 N
Now, calculate the static frictional force:
μ_friction = 0.660
F_friction = (0.660) * (627.2 N)
F_friction ≈ 413.09 N
The static frictional force exerted by the floor on the refrigerator can be expressed in vector form as:
F_friction = +413.09i
(b) The maximum force that needs to be applied before the refrigerator starts to move is equal to the maximum value of static friction, which is:
F_max = μ_friction * N
F_max = (0.660) * (627.2 N)
F_max ≈ 414.15 N
So, the magnitude of the maximum force you need to apply before the refrigerator starts to move is approximately 414.15 N.
To find the static frictional force exerted on the refrigerator, we need to multiply the coefficient of static friction by the normal force.
(a) The static frictional force can be calculated using the equation:
f_static = μ_static * N
where f_static is the static frictional force, μ_static is the coefficient of static friction, and N is the normal force.
The normal force is equal to the weight of the refrigerator, which can be calculated as:
N = m * g
where m is the mass of the refrigerator and g is the acceleration due to gravity.
Given:
m = 64.0 kg
g = 9.8 m/s^2 (approximation for the acceleration due to gravity)
Calculating the normal force:
N = 64.0 kg * 9.8 m/s^2 = 627.2 N
Now we can calculate the static frictional force:
f_static = 0.660 * 627.2 N
To express the static frictional force in vector form, we need to consider the direction of the applied force. In this case, the applied force is given as:
F = +214i - 171k N
Since the static frictional force will act in the opposite direction to the applied force, the vector form of the static frictional force would be:
f_static = -214i + 171k N
(b) The magnitude of the maximum force that needs to be applied before the refrigerator starts to move is equal to the product of the coefficient of static friction and the normal force.
f_max = μ_static * N
Using the same values for μ_static and N as calculated in part (a), we can find:
f_max = 0.660 * 627.2 N
Therefore, the magnitude of the maximum force that needs to be applied is approximately:
|f_max| = 0.660 * 627.2 N