276-kg glider is being pulled by a 1 950-kg jet along a horizontal runway
with an acceleration of aS 5 2.20 m/s2 to the right as in Figure below. Find
(a) the thrust provided by the jet’s engines and (b) the magnitude of the
tension in the cable connecting the jet and glider
1. A 276-kg glider is being pulled by a 1 950-kg jet along a horizontal runway
with an acceleration of aS 5 2.20 m/s2 to the right as in Figure below. Find
(a) the thrust provided by the jet’s engines and (b) the magnitude of the
tension in the cable connecting the jet and glider.
To find the answers, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(a) To find the thrust provided by the jet's engines, we need to calculate the net force acting on the jet.
Net force = mass of the jet × acceleration of the jet
Given:
Mass of the jet (m_jet) = 1,950 kg
Acceleration of the jet (a_jet) = 2.20 m/s²
Net force = m_jet × a_jet
Net force = 1,950 kg × 2.20 m/s²
Net force = 4,290 N
Therefore, the thrust provided by the jet's engines is 4,290 N.
(b) To find the magnitude of the tension in the cable connecting the jet and glider, we need to consider the net force acting on the glider.
Net force = mass of the glider × acceleration of the glider
Given:
Mass of the glider (m_glider) = 276 kg
Acceleration of the glider (a_glider) = 2.20 m/s²
Net force = m_glider × a_glider
Net force = 276 kg × 2.20 m/s²
Net force = 607.2 N
The tension in the cable is equal to the net force acting on the glider.
Therefore, the magnitude of the tension in the cable connecting the jet and glider is 607.2 N.
To find the thrust provided by the jet's engines and the tension in the cable connecting the jet and glider, we can make use of Newton's second law of motion, which states that the net force applied to an object is equal to the product of its mass and acceleration.
(a) Thrust provided by the jet's engines:
The net force acting on the glider is the tension force from the cable pulling it forward, minus the force of friction opposing its motion. We can set up an equation using Newton's second law:
Net force = Mass * Acceleration
Since there is no vertical motion mentioned in the problem statement, we only need to consider the horizontal forces. The only horizontal force acting on the glider is the thrust provided by the jet's engines. So, we can write the equation as:
Thrust - Force of friction = Mass of the glider * Acceleration
The force of friction can be calculated using the formula:
Force of friction = Coefficient of friction * Normal force
For a glider on a horizontal surface, the normal force is equal to the weight of the glider, which can be calculated as:
Normal force = Mass of the glider * Acceleration due to gravity
Substituting these values into our equation, we have:
Thrust - (Coefficient of friction * Mass of the glider * Acceleration due to gravity) = Mass of the glider * Acceleration
Now we can solve for the thrust by isolating the variable:
Thrust = Mass of the glider * (Acceleration + Coefficient of friction * Acceleration due to gravity)
(b) Magnitude of the tension in the cable:
The tension force in the cable connecting the jet and glider is equal to the thrust provided by the jet's engines. Therefore, the magnitude of the tension in the cable is also equal to the magnitude of the thrust.
So, for part (b), we can use the same value we calculated for the thrust in part (a).
Note: To calculate the force of friction, you would need to know the coefficient of friction between the glider and the runway surface. This information is not provided in the question, so we cannot obtain an exact numerical value for the thrust and tension without it.