# An object with a mass of #7 kg# is on a surface with a kinetic friction coefficient of # 8 #. How much force is necessary to accelerate the object horizontally at # 21 m/s^2#?

Newton's second law of motion states that the sum of the forces acting on an object is equal to its mass multiplied by its acceleration.

Mathematically speaking,

In your case, we will start off by letting the up and forward directions be positive.

Step 1 List out all the forces acting on the object.

So we are left with,

Step 4 Plug in your known values.

Solve.

Rounding off the answer to one significant figure,

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To calculate the force necessary to accelerate the object horizontally at 21 m/s^2, you can use the formula: ( F = m \times a ), where ( F ) is the force, ( m ) is the mass of the object, and ( a ) is the acceleration.

Given:

- Mass (( m )) = 7 kg
- Acceleration (( a )) = 21 m/s^2

Substitute the given values into the formula: ( F = 7 , \text{kg} \times 21 , \text{m/s}^2 )

Calculate: ( F = 147 , \text{N} )

So, the force necessary to accelerate the object horizontally at 21 m/s^2 is 147 Newtons.

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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.

- 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 # 7 m/s^2#?
- A box with an initial speed of #4 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/6 # and an incline of #pi /3 #. How far along the ramp will the box go?
- 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 # 8 N # of force, what is the net force on the object?
- How fast will an object with a mass of #16 kg# accelerate if a force of #68 N# is constantly applied to it?
- A box with an initial speed of #1 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #5/4 # and an incline of #(3 pi )/4 #. How far along the ramp will the box go?

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