# If an object is moving at #4 ms^-1# over a surface with a kinetic friction coefficient of #u_k=3 /g#, how far will the object continue to move?

The distance is

According to Newton's Second Law

Apply the equation of motion,

The distance is

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To find out how far the object will continue to move, we can use the equation for kinetic friction:

(f_k = \mu_k \times N)

Where:

- (f_k) is the force of kinetic friction
- (\mu_k) is the coefficient of kinetic friction
- (N) is the normal force exerted on the object

Since the object is moving horizontally, the normal force ((N)) is equal to the gravitational force acting on the object:

(N = mg)

Where:

- (m) is the mass of the object
- (g) is the acceleration due to gravity (approximately (9.8 m/s^2))

Given that the coefficient of kinetic friction ((\mu_k)) is (3/g), we can substitute the values into the equation:

(f_k = (3/g) \times mg)

(f_k = 3m)

The force of kinetic friction ((f_k)) is also equal to the mass of the object multiplied by its acceleration ((ma)). Since the object is moving at a constant velocity, the acceleration is (0).

(f_k = ma)

(3m = 0)

Thus, the object will continue to move indefinitely because the force of kinetic friction is insufficient to stop it. Therefore, there is no specific distance it will travel over the surface.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Your body applies force to the ground as weight. If you weigh 450 newtons and carry a backpack that weighs 45 newtons, what is the net force applied downward to the ground?
- Two masses are in contact on a horizontal frictionless surface. A horizontal force is applied to #M_1# and a second horizontal force is applied to #M_2# in the opposite direction. What is the magnitude of the contact force between the masses?
- A truck pulls boxes up an incline plane. The truck can exert a maximum force of #5,700 N#. If the plane's incline is #(2 pi )/3 # and the coefficient of friction is #8/5 #, what is the maximum mass that can be pulled up at one time?
- An object with a mass of #1 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x-x+3 #. How much work would it take to move the object over #x in [1, 4], where x is in meters?
- What is the coefficient of friction?

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