A helicopter of mass M is lowering a truck of mass m onto the deck of a ship.
A) At first, the helicopter and the truck move downward together ( the length of the cable doesn’t change). If their downward speed is decreasing at a rate of 0.10g, what is the tension in the cable?
B) As the truck gets closer to the deck, the helicopter stops moving downward. While it hovers, it lets out the cable so that the truck is still moving downward. If the truck’s downward speed is decreasing at a rate of 0.10g, while the helicopter is at rest, what is the tension in the cable?
I know that the tension on the cable is equal to gravitational forces exerted by earth on the truck, T= (GMem)/r^2. But I couldn’t use this formula because r is not found. Also, what does the g by the given above numbers mean. Is it grams, 9.8, or does it represent something else?
A) At first, the helicopter and the truck move downward together ( the length of the cable doesn’t change). If their downward speed is decreasing at a rate of 0.10g, what is the tension in the cable?
B) As the truck gets closer to the deck, the helicopter stops moving downward. While it hovers, it lets out the cable so that the truck is still moving downward. If the truck’s downward speed is decreasing at a rate of 0.10g, while the helicopter is at rest, what is the tension in the cable?
I know that the tension on the cable is equal to gravitational forces exerted by earth on the truck, T= (GMem)/r^2. But I couldn’t use this formula because r is not found. Also, what does the g by the given above numbers mean. Is it grams, 9.8, or does it represent something else?
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Since the downward speed of the helicopter and truck is decreasing, an upward force must be causing each of them to decelerate. The propellers of the helicopter are causing the helicopter to decelerate. The tension in the cable is causing the truck to decelerate.
g = 9.8 m/s^2
0.1 g = 0.98 m/s^2
Initially, the helicopter and truck are moving downward together. Since the cable is attached to the helicopter and truck, the cable is moving at the same speed as they are. So the initial tension in the cable is 0 N.
When their downward speed is decreasing 0.98 m/s each second, the tension is cable is causing the decrease of the truck’ speed. For the speed of the truck to decrease, the cable must be exerting an upward force on the truck.
If you draw a free body diagram of the truck, you will see that the truck has 2 vertical forces on it. The tension in the cable is an upward force, and its weight is a downward force. For the downward speed of the truck to decrease, the upward tension force must be greater than the weight of the truck.
The difference of these 2 vertical forces is causing the downward speed of the helicopter to decrease 0.98 m/s each second.
g = 9.8 m/s^2
0.1 g = 0.98 m/s^2
Initially, the helicopter and truck are moving downward together. Since the cable is attached to the helicopter and truck, the cable is moving at the same speed as they are. So the initial tension in the cable is 0 N.
When their downward speed is decreasing 0.98 m/s each second, the tension is cable is causing the decrease of the truck’ speed. For the speed of the truck to decrease, the cable must be exerting an upward force on the truck.
If you draw a free body diagram of the truck, you will see that the truck has 2 vertical forces on it. The tension in the cable is an upward force, and its weight is a downward force. For the downward speed of the truck to decrease, the upward tension force must be greater than the weight of the truck.
The difference of these 2 vertical forces is causing the downward speed of the helicopter to decrease 0.98 m/s each second.
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