# An object with a mass of #12 kg# is on a surface with a kinetic friction coefficient of # 15 #. How much force is necessary to accelerate the object horizontally at # 4 m/s^2#?

The force is

The frictional force is

The normal force is

So,

Resolving in the horizontal direction

We apply Newton's second Law

So,

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To accelerate the object horizontally at 4 m/s^2, a force of 72 N is necessary.

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To calculate the force necessary to accelerate the object horizontally at 4 m/s^2, we'll use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). However, we also need to account for friction. The force of friction is given by the product of the coefficient of kinetic friction (μ) and the normal force (N) acting on the object.

First, let's calculate the force of friction using the formula:

Frictional force (F_friction) = coefficient of kinetic friction (μ) * normal force (N)

Since the object is on a horizontal surface, the normal force is equal to the gravitational force acting on it, which is given by:

Normal force (N) = mass (m) * gravitational acceleration (g)

Then, we can find the frictional force using the given coefficient of kinetic friction.

After finding the frictional force, we can use Newton's second law to calculate the net force required to accelerate the object:

Net force (F_net) = mass (m) * acceleration (a)

Since the force of friction opposes the direction of motion, the net force will be the sum of the force needed to overcome friction and the force required for acceleration.

Finally, the total force required will be the sum of the force needed to overcome friction and the force required for acceleration.

Total force (F_total) = F_friction + F_net

By substituting the calculated values into these equations, we can find the total force necessary to accelerate the object horizontally at 4 m/s^2.

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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.

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- An object with a mass of #8 kg# is on a plane with an incline of # - pi/12 #. If it takes #8 N# to start pushing the object down the plane and #2 N# to keep pushing it, what are the coefficients of static and kinetic friction?
- An object with a mass of #8 kg# is on a plane with an incline of #pi/8 #. If the object is being pushed up the plane with # 5 N # of force, what is the net force on the object?

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