Final answer:
The tension in the crane's cable when lifting a 650kg car at a constant velocity of 1.30m/s is equal to the weight of the car due to gravity, which is 6376.5 N. Thus, the closest given option is 6,500 N.
Step-by-step explanation:
To find the tension in the crane's cable when lifting a 650kg car straight up at 1.30m/s, we can assume that the system is in equilibrium since the velocity is constant and there are no accelerations involved. This means the net force acting on the car is zero, and the only forces acting on the car are the gravitational force (weight) and the tension in the cable.
The force due to gravity is calculated as weight (W) = mass (m) × acceleration due to gravity (g), which is W = 650 kg × 9.81 m/s² = 6376.5 N. Since the car is not accelerating, the tension in the cable (T) must be equal to the weight of the car to maintain the constant velocity.
Therefore, the tension in the crane's cable is 6376.5 N, which is closest to Option 3: 6,500 N from the given options.