# 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 # 3 N # of force, what is the net force on the object?

The net force is

Taking the direction up and parallel to the plane as positive

Let the force pushing the object be

Then the net force on the object is

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The net force on the object can be calculated using the formula: ( F_{\text{net}} = F_{\text{applied}} - F_{\text{gravity}} ). First, find the force of gravity acting on the object using the formula: ( F_{\text{gravity}} = m \cdot g ), where ( m ) is the mass of the object (8 kg) and ( g ) is the acceleration due to gravity (approximately 9.8 m/s²). Then, calculate the component of the applied force acting against gravity along the incline using ( F_{\text{applied_parallel}} = F_{\text{applied}} \cdot \sin(\text{inclined angle}) ). Finally, subtract the force of gravity from the component of the applied force along the incline to find the net force on the object.

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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.

- A box with an initial speed of #3 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #8/7 # and an incline of #( pi )/4 #. How far along the ramp will the box go?
- An object with a mass of #5 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?
- A box with an initial speed of #12 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #8/7 # and an incline of #( pi )/4 #. How far along the ramp will the box go?
- An object with a mass of # 5 kg# is lying still on a surface and is compressing a horizontal spring by #2 m#. If the spring's constant is # 8 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- 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 # 32 m/s^2#?

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