A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 112-kg laser sensor which measures the thickness of the ice (see the drawing). The helicopter and the sensor move only in the horizontal direction and have a horizontal acceleration of magnitude 2.52 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.
Ignoring air-resistance on the sensor.
Horizontal acceleration, ah = 2.52 m/s²
Horizontal component of force
=m*ah
Weight of sensor = mg
Since the directions of m*ah and mg are orthogonal (at 90°), the vector sum is required for the tension of the cable
T=sqrt((mg)^2+(m*ah)^2)
=m*sqrt(9.81²+2.52²)
=m*10.12
=1134 N
Well, it sounds like this helicopter has a real "ice" job. But let's get to the question at hand.
To find the tension in the cable towing the sensor, we need to consider the forces acting on the sensor. There are three forces: the force of gravity pulling it down, the tension in the cable pulling it horizontally, and the horizontal component of the sensor's weight.
Since the sensor is moving horizontally at a constant altitude, its vertical acceleration is zero. This means that the sum of the vertical forces must be zero. Therefore, the vertical component of the sensor's weight must be equal in magnitude and opposite in direction to the tension in the cable.
Now, let's find the horizontal component of the sensor's weight. Since the sensor has a mass of 112 kg and the acceleration is 2.52 m/s², we can calculate the horizontal component of the sensor's weight using Newton's second law:
F = m * a
F = 112 kg * 2.52 m/s²
F = 282.24 N
So, the tension in the cable towing the sensor is 282.24 N. But you know what they say, "No tension, no cry!"
To find the tension in the cable towing the sensor, we need to consider the forces acting on the sensor in the horizontal direction.
The only horizontal force acting on the sensor is the tension in the cable. We can use Newton's second law to find the tension.
Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension in the cable, the mass is the mass of the sensor (112 kg), and the acceleration is the horizontal acceleration of the helicopter (2.52 m/s^2).
So we can write:
Tension = mass x acceleration
Tension = 112 kg x 2.52 m/s^2
Tension = 282.24 N
Therefore, the tension in the cable towing the sensor is 282.24 N.
To find the tension in the cable towing the sensor, we can use Newton's second law of motion.
First, let's consider the forces acting on the sensor. In the horizontal direction, the only force is the tension in the cable. However, in the vertical direction, there are two forces: the weight of the sensor and the tension in the cable.
Using Newton's second law in the horizontal direction, we have:
Tension = mass of the sensor * horizontal acceleration
T = 112 kg * 2.52 m/s^2
T = 282.24 N
So, the tension in the cable towing the sensor is 282.24 Newtons.