A 276-kg glider is being pulled by a 1 950-kg airplane along a hori zontal runway with an acceleration of vec a =2.20 m/s^ 2 to the right as in Figure P4.33. Find (a) the thrust provided by the airplane's propellers and (b) the magnitude of the tensicn in the cable connecting the airplane and glider.

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To find the thrust provided by the airplane's propellers (part a), we need to apply Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration:

Net Force = Mass × Acceleration

In this case, the glider is being pulled by the airplane, so the net force acting on the glider is equal to the tension in the cable connecting the airplane and the glider. Therefore:

Tension = Mass × Acceleration

To find the tension in the cable connecting the airplane and glider (part b), we need to consider the forces acting on the glider. There are two forces to consider:

1. The force of gravity acting vertically downwards, which can be calculated by multiplying the mass of the glider by the acceleration due to gravity (9.8 m/s^2).
Force of Gravity = Mass × Acceleration due to Gravity

2. The tension in the cable, which is acting horizontally to the right.

Since the glider is being pulled to the right with an acceleration of 2.20 m/s^2, the net force acting on the glider in the horizontal direction is equal to the tension in the cable minus the force of friction (assuming no other horizontal forces).

Therefore:

Net Force = Tension - Force of Friction

Since the glider and airplane are moving together without slipping, the force of friction can be calculated by multiplying the coefficient of kinetic friction (μ) between the glider and the runway by the normal force (which is equal to the force of gravity).

Force of Friction = Coefficient of Kinetic Friction × Force of Gravity

To find the coefficient of kinetic friction in this case, we need to use the fact that the acceleration of the glider is equal to the acceleration of the airplane, as they are connected by the cable:

Acceleration = (Tension - Force of Friction) / Glider Mass

By rearranging the equation and substituting the values we know, we can solve for the tension:

Tension = (Glider Mass × Acceleration) + (Coefficient of Kinetic Friction × Glider Mass × Acceleration due to Gravity)

Once we have both the tension and thrust, we can substitute these values into the equations provided to find the answers to (a) and (b) respectively.