A 7000 kg helicopter accelerates upward at 0.70 m/s/s while lifting a 1000 kg car to a mountaintop for a TV commercial photo shoot.
-What tension must the cable be able to withstand without breaking?
Tension=masscar(g+a)
To find the tension in the cable, we need to calculate the net force acting on the helicopter and the car. Here's how to do it step-by-step:
Step 1: Calculate the force exerted by the helicopter:
The force exerted by the helicopter is given by Newton's second law:
Force = mass * acceleration
Given:
Mass of the helicopter (m1) = 7000 kg
Acceleration (a) = 0.70 m/s^2
Force1 = m1 * a
Force1 = 7000 kg * 0.70 m/s^2
Force1 = 4900 N
So, the force exerted by the helicopter is 4900 N.
Step 2: Calculate the force exerted by the car:
The force exerted by the car is also given by Newton's second law:
Force = mass * acceleration
Given:
Mass of the car (m2) = 1000 kg
Acceleration (a) = 0.70 m/s^2
Force2 = m2 * a
Force2 = 1000 kg * 0.70 m/s^2
Force2 = 700 N
So, the force exerted by the car is 700 N.
Step 3: Calculate the total force exerted by the cable:
The cable needs to support the weight of both the helicopter and the car, so the total force exerted by the cable is the sum of the forces exerted by the helicopter and the car:
Total Force = Force1 + Force2
Total Force = 4900 N + 700 N
Total Force = 5600 N
Therefore, the tension in the cable must be able to withstand a force of 5600 N without breaking.
To determine the tension in the cable, we need to consider the forces acting on the helicopter and car system.
1. Start by calculating the force required to lift the helicopter itself:
The force required to accelerate an object can be calculated using Newton's second law: F = m * a, where F is the force, m is the mass, and a is the acceleration.
The mass of the helicopter is given as 7000 kg, and the acceleration is 0.70 m/s^2.
So, the force required to lift the helicopter alone is F_helicopter = m_helicopter * a = 7000 kg * 0.70 m/s^2.
2. Calculate the force required to lift the car:
Similarly, the force required to accelerate the car is F_car = m_car * a = 1000 kg * 0.70 m/s^2.
3. Sum up the forces:
The total force required would be the sum of the forces for the helicopter and the car: F_total = F_helicopter + F_car.
4. Calculate the tension in the cable:
The tension in the cable would be equal to the total force required to lift both the helicopter and the car: Tension_cable = F_total.
Now, let's calculate the tension in the cable step by step:
F_helicopter = 7000 kg * 0.70 m/s^2 = 4900 N (Newtons)
F_car = 1000 kg * 0.70 m/s^2 = 700 N (Newtons)
F_total = F_helicopter + F_car
F_total = 4900 N + 700 N
F_total = 5600 N (Newtons)
Therefore, the tension in the cable must be able to withstand 5600 Newtons without breaking.