# A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,500 N#. If the plane's incline is #(5 pi )/8 # and the coefficient of friction is #7/6 #, 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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To calculate the maximum mass that can be pulled up the incline plane, we need to consider the force of gravity, the force exerted by the truck, and the frictional force. The force of gravity pulling the mass down the incline can be calculated using the formula F_gravity = m * g * sin(theta), where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and theta is the angle of the incline. The frictional force opposing the motion can be calculated using the formula F_friction = coefficient of friction * N, where N is the normal force exerted by the incline on the mass. The normal force can be calculated using the formula N = m * g * cos(theta). We'll set up the equations and solve for the maximum mass:

F_gravity = F_truck - F_friction m * g * sin(theta) = F_truck - (coefficient of friction * m * g * cos(theta))

Now, we plug in the given values:

m * 9.8 * sin((5 * pi) / 8) = 3500 - (7/6 * m * 9.8 * cos((5 * pi) / 8))

Solving for m:

m = (3500) / (9.8 * sin((5 * pi) / 8) + (7/6 * 9.8 * cos((5 * pi) / 8)))

Calculating this gives us the maximum mass that can be pulled up the incline plane.

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The maximum mass that can be pulled up the incline plane at one time is approximately 392.70 kg.

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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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