A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 118-kg laser sensor that measures the thickness of the ice (see the drawing). The helicopter and the sensor both move only in the horizontal direction and have a horizontal acceleration of magnitude 2.55 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.
To find the tension in the cable towing the sensor, we can start by analyzing the forces acting on the sensor in the horizontal direction.
The horizontal force acting on the sensor is provided by the tension in the cable. In the absence of air resistance, this force is the only horizontal force acting on the sensor.
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration is the horizontal acceleration provided to both the helicopter and the sensor, which is 2.55 m/s^2.
The net force acting on the sensor is given by the equation:
Net force = mass of the sensor * acceleration
The mass of the sensor is given as 118 kg. Substituting these values into the equation, we have:
Net force = (118 kg) * (2.55 m/s^2)
Next, we can determine the tension in the cable by setting the net force equal to the force of tension:
Tension in the cable = Net force
Therefore, the tension in the cable towing the sensor is equal to the net force acting on the sensor, which is given by the equation above.
Solving the equation:
Tension in the cable = (118 kg) * (2.55 m/s^2)
Calculating this expression gives us the value for the tension in the cable towing the sensor.