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 #(5 pi )/12 # and the coefficient of friction is #5/12 #, what is the maximum mass that can be pulled up at one time?

Answer 1

The mass is #=342.1kg#

Resolving in the direction parallel to the plane #↗^+#

Let the force exerted by the truck be #=FN#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N#

The normal force is #N=mgcostheta#

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

#m=F/(g(mucostheta+sintheta))#

#=3600/(9.8(5/12*cos(5/12pi))+sin(5/12pi))#

#=342.1kg#

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Answer 2

To find the maximum mass that can be pulled up the incline, we need to consider the forces acting on the system. The maximum force the truck can exert, denoted by ( F_{\text{max}} ), is 3,600 N.

The force due to gravity acting on the mass being pulled up the incline is given by ( mg ), where ( m ) is the mass and ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 )).

The component of the weight of the mass parallel to the incline is ( mg \sin(\theta) ), where ( \theta ) is the angle of incline.

The force of friction, ( f_{\text{friction}} ), is given by the product of the coefficient of friction ( \mu ) and the normal force ( N ).

Since the mass is being pulled up the incline with the maximum force, the force of friction will also be at its maximum, which is ( \mu N ).

Considering that the force exerted by the truck must overcome both the component of the weight parallel to the incline and the force of friction, we have:

[ F_{\text{max}} = mg \sin(\theta) + \mu N ]

Solving for ( m ), we get:

[ m = \frac{F_{\text{max}} - \mu N}{g \sin(\theta)} ]

Given that ( F_{\text{max}} = 3,600 , \text{N} ), ( \theta = \frac{5\pi}{12} ), and ( \mu = \frac{5}{12} ), we can substitute these values into the equation to find the maximum mass that can be pulled up at one time.

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Answer from HIX Tutor

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.

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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