# A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,600 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #9/4 #, what is the maximum mass that can be pulled up at one time?

The mass is

Resolving in the direction parallel to the plane

Let the force exerted by the truck be

Let the frictional force be

The coefficient of friction

The normal force is

The angle of the plane is

The acceleration due to gravity is

Therefore,

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The maximum mass that can be pulled up at one time is ( m = \frac{F_{\text{max}} - F_{\text{friction}}}{g \sin(\theta)} ), where ( F_{\text{max}} ) is the maximum force the truck can exert, ( F_{\text{friction}} ) is the maximum frictional force, ( g ) is the acceleration due to gravity, and ( \theta ) is the angle of the incline. The maximum frictional force is ( F_{\text{friction}} = \mu \cdot F_{\text{normal}} ), where ( \mu ) is the coefficient of friction and ( F_{\text{normal}} ) is the normal force. Given ( F_{\text{max}} = 3600 ) N, ( \mu = \frac{9}{4} ), ( \theta = \frac{3\pi}{8} ), and ( g = 9.8 ) m/s(^2), we can calculate ( F_{\text{friction}} ) and then the maximum mass ( m ).

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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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