# An object with a mass of #5 kg# is on a surface with a kinetic friction coefficient of # 4 #. How much force is necessary to accelerate the object horizontally at # 3 m/s^2#?

The force is

The force of friction

Next,

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To calculate the force necessary to accelerate the object horizontally at 3 m/s^2, you can use the equation:

[ F_{\text{net}} = m \cdot a + F_{\text{friction}} ]

Where ( F_{\text{net}} ) is the net force, ( m ) is the mass of the object (5 kg), ( a ) is the acceleration (3 m/s^2), and ( F_{\text{friction}} ) is the force of friction.

To find ( F_{\text{friction}} ), you can use the equation:

[ F_{\text{friction}} = \mu \cdot N ]

Where ( \mu ) is the coefficient of kinetic friction (0.4) and ( N ) is the normal force exerted on the object by the surface. Since the object is on a horizontal surface, the normal force is equal to the gravitational force acting on the object, which is ( m \cdot g ), where ( g ) is the acceleration due to gravity (approximately 9.8 m/s^2).

Plugging in the values:

[ F_{\text{friction}} = 0.4 \cdot (5 , \text{kg}) \cdot (9.8 , \text{m/s}^2) ]

[ F_{\text{friction}} = 19.6 , \text{N} ]

Now, plug this value into the first equation:

[ F_{\text{net}} = (5 , \text{kg}) \cdot (3 , \text{m/s}^2) + 19.6 , \text{N} ]

[ F_{\text{net}} = 15 , \text{N} + 19.6 , \text{N} ]

[ F_{\text{net}} = 34.6 , \text{N} ]

So, the force necessary to accelerate the object horizontally at 3 m/s^2 is 34.6 N.

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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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