Calculating Static Frictional Force on an incline

In summary, a car with a mass of 1680 kg is parked on a road inclined at 17°. The normal force, which is equal to the weight of the car multiplied by the cosine of the angle, can be found by multiplying the mass by 9.8 and then cosine of 17. To find the static friction force, which is balanced by the normal force, you do not need the coefficient of friction. Instead, you can use the conditions for static equilibrium and write down the equations of equilibrium for all the forces acting on the car. This will allow you to solve for the static friction force.
  • #1
Shadow236
18
0

Homework Statement


A car (m = 1680 kg) is parked on a road that rises 17° above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?



Homework Equations


FsMAX = Mu*FN or in this case: FsMAX = Mu*mg*cos(17)



The Attempt at a Solution


I found (a), the normal force by finding mg (1680 * 9.8) and then multiplying that by cos(17) because of the incline. My problem is finding the static frictional force because there is no coefficient given. I've tried to find the coefficient by using the normal force, but I still end up with two unknowns... 16464 (FN) = Fs/Mu.
 
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  • #2
Shadow236 said:
I found (a), the normal force by finding mg (1680 * 9.8) and then multiplying that by cos(17) because of the incline.
Good.

My problem is finding the static frictional force because there is no coefficient given. I've tried to find the coefficient by using the normal force, but I still end up with two unknowns... 16464 (FN) = Fs/Mu.
You are asked to find the actual static friction force, not the maximum value between the surfaces. Hint: You don't need the coefficient, just the conditions for static equilibrium.
 
  • #3
Because the car is parked, it is stationary, that is to say, in equilibrium. So the force of static friction is balanced by some other force. What is this force? Can you find it?
 
  • #4
voko said:
Because the car is parked, it is stationary, that is to say, in equilibrium. So the force of static friction is balanced by some other force. What is this force? Can you find it?
Are they the Normal Force and the weight of the car?
 
  • #5
Isn't the normal force perpendicular to the force of friction? How can they balance each other then?

It is probably best to list all the forces, choose a coordinate system, and write down the equations of equilibrium.
 

Related to Calculating Static Frictional Force on an incline

1. What is static frictional force?

Static frictional force is the force that resists the relative motion between two surfaces in contact with each other. It acts in the opposite direction to the applied force and prevents objects from sliding or moving when a force is applied.

2. How is the static frictional force calculated?

The static frictional force can be calculated using the formula F = μN, where F is the static frictional force, μ is the coefficient of static friction, and N is the normal force.

3. What is the coefficient of static friction?

The coefficient of static friction is a dimensionless constant that represents the amount of force required to initiate motion between two surfaces in contact. It varies depending on the materials and surface conditions of the objects in contact.

4. How does the incline affect the calculation of static frictional force?

The incline affects the calculation of static frictional force because it changes the normal force acting on the object. The normal force is the force perpendicular to the surface of contact and is equal to the weight of the object in the absence of other forces. As the incline increases, the normal force decreases, resulting in a lower static frictional force.

5. What are some real-life applications of calculating static frictional force on an incline?

Calculating static frictional force on an incline is important in engineering and design, such as in the construction of ramps, roads, and railways. It is also used in physics experiments, such as determining the coefficient of static friction between different materials. Additionally, understanding static frictional force on an incline can help prevent accidents and injuries in situations where objects are at risk of sliding or rolling down inclines.

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