Acceleration given kinetic friction

In summary, acceleration given kinetic friction is the change in velocity of an object as it moves across a surface with kinetic friction, and is influenced by factors such as mass, coefficient of kinetic friction, and applied force. It is calculated using the formula a = F_net / m - u_k, where a is acceleration, F_net is net force, m is mass, and u_k is coefficient of kinetic friction. This is different from acceleration given static friction, which is the acceleration at the point where an object is about to start moving on a surface with static friction. The coefficient of kinetic friction affects acceleration given kinetic friction by increasing the amount of force needed to accelerate the object. It can also result in negative acceleration if the net force acts in
  • #1
IAmSparticus
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1. A crate is sliding down a ramp that is inclined at an angle of 51.1° above the horizontal. The coefficient of kinetic friction between the crate and the ramp surface is 1.171. Find the acceleration of the moving crate.


2. Fnet = mass of object x acceleration


3. Sine I don't have the mass, I'm not sure what to plug into the equation. Can someone walk me through how to solve it?
 
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  • #3


I can help you solve this problem. First, we need to understand the concept of acceleration and its relationship with forces. Acceleration is defined as the rate of change of an object's velocity over time. This means that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is represented by the equation Fnet = ma, where Fnet is the net force, m is the mass of the object, and a is the acceleration.

In this scenario, the only force acting on the crate is the force of friction, which is given by μkN, where μk is the coefficient of kinetic friction and N is the normal force. The normal force is the force exerted by the ramp on the crate perpendicular to the surface. Since the crate is on an inclined plane, the normal force can be calculated using the equation N = mgcosθ, where m is the mass of the crate, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of inclination (51.1°).

Now, we can plug these values into the equation Fnet = ma and solve for the acceleration. The net force in this case is the force of friction, so we have μkN = ma. Substituting the values for μk and N, we get μkmgcosθ = ma. We can then rearrange the equation to solve for the acceleration, which gives us a = μkgcosθ/m.

To find the mass of the crate, we can use the given information that the coefficient of kinetic friction is 1.171. This means that μk = 1.171. We can also assume that the crate has a standard mass of 1 kg. Therefore, we can plug in these values and solve for the acceleration, which gives us a = 1.171(1 kg)(9.8 m/s^2)cos(51.1°)/1 kg = 5.89 m/s^2.

In summary, the acceleration of the crate sliding down the ramp is 5.89 m/s^2. I hope this explanation helps you understand how to solve problems involving acceleration and friction.
 

1. What is acceleration given kinetic friction?

Acceleration given kinetic friction is the rate of change of velocity of an object as it moves across a surface with kinetic friction. It is influenced by factors such as the mass of the object, the coefficient of kinetic friction, and the applied force.

2. How is acceleration given kinetic friction calculated?

The formula for acceleration given kinetic friction is a = F_net / m - u_k, where a is the acceleration, F_net is the net force acting on the object, m is the mass of the object, and u_k is the coefficient of kinetic friction.

3. What is the difference between acceleration given kinetic friction and acceleration given static friction?

Acceleration given kinetic friction is the acceleration of an object as it moves across a surface with kinetic friction, while acceleration given static friction is the acceleration of an object at the point where it is just about to start moving on a surface with static friction.

4. How does the coefficient of kinetic friction affect acceleration given kinetic friction?

The coefficient of kinetic friction is a measure of the amount of friction between two surfaces in contact when one is in motion. A higher coefficient of kinetic friction will result in a lower acceleration given kinetic friction, as more force is required to overcome the friction and accelerate the object.

5. Can acceleration given kinetic friction be negative?

Yes, acceleration given kinetic friction can be negative. This occurs when the net force acting on the object is in the opposite direction of its motion, resulting in a decrease in velocity or deceleration.

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