A stationary 2.0 kg object is located on a table near the surface of the earth. The coefficient static friction between the surface is .80 and the coefficient of the kinetic friction is 0.65. A horizontal force of 5N is applied to the object. Determine the force of friction. Determine the accelaration of the object. How should we change the magnitude of the horizontal applied force to get an acceleration of 1.5 m/s^2? What is the friction force at that acceleration
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To determine the force of friction, we need to consider whether the object is at rest or in motion. Since the object is stationary, we will first calculate the maximum force of static friction using the coefficient of static friction.
The maximum force of static friction (Fs_max) can be calculated using the formula:
Fs_max = coefficient of static friction * normal force
where the normal force is equal to the weight of the object due to gravity, which can be calculated using the formula:
Normal force = mass * acceleration due to gravity
Plugging in the given values, we have:
Mass = 2.0 kg
Coefficient of static friction (μs) = 0.80
Acceleration due to gravity (g) = 9.8 m/s²
Normal force = mass * acceleration due to gravity
= 2.0 kg * 9.8 m/s²
= 19.6 N
Now we can determine the maximum force of static friction:
Fs_max = coefficient of static friction * normal force
= 0.80 * 19.6 N
= 15.68 N
Since the applied force of 5N is less than the maximum force of static friction (15.68 N), the object remains at rest, and the force of friction is equal to the applied force, which is 5 N.
Next, let's determine the acceleration of the object when the applied force is 5N. We can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration:
Force net = mass * acceleration
In this case, the net force is the difference between the applied force and the force of friction:
Force net = applied force - force of friction
= 5 N - 5 N
= 0 N
Therefore, the net force is zero, meaning the acceleration is also zero. The object remains at rest.
To achieve an acceleration of 1.5 m/s², we need to increase the net force acting on the object. Using the same formula as above, we can rearrange it to solve for the required applied force (F_applied):
Force net = mass * acceleration
F_applied - force of friction = mass * acceleration
Rearranging the equation:
F_applied = mass * acceleration + force of friction
Plugging in the values:
Mass = 2.0 kg
Acceleration = 1.5 m/s²
Force of friction = 5 N (since the object is still on the same surface)
F_applied = 2.0 kg * 1.5 m/s² + 5 N
= 3.0 N + 5 N
= 8 N
Therefore, to achieve an acceleration of 1.5 m/s², the magnitude of the horizontal applied force should be increased to 8 N.
Finally, to calculate the friction force at this new acceleration, we can subtract the applied force from the force of friction:
Friction force = force of friction - applied force
= 5 N - 8 N
= -3 N
Since the friction force is negative, it indicates that the direction of the force is opposite to the applied force. In other words, the friction force acts in the opposite direction and opposes the applied force. Therefore, the friction force at an acceleration of 1.5 m/s² is 3 N in the opposite direction of motion.