Calculate Forces on Parachute & Person: Parachute Homework

• A_lilah
In summary, a 78 kg person is parachuting with a downward acceleration of 2.8 m/s2, while the parachute has a mass of 5.4 kg. The net force on the person is 218.4 N downward, with a tension of 982.8 N and a weight of 764.4 N. The net force on the parachute is 15.12 N downward, with an air resistance of 1050.84 N and a tension of 982.8 N. The total downward force on the parachute is 1747.2 N. The correct answers are: (a) 1050.84 N for the upward force exerted by the air on the parachute, and (b
A_lilah

Homework Statement

A 78 kg person is parachuting and experiencing a downward acceleration of 2.8 m/s2. The mass of the parachute is 5.4 kg.
(a) What upward force is exerted on the open parachute by the air?
(b) What downward force is exerted by the person on the parachute?

Fnet = ma

The Attempt at a Solution

Forces on parachute:
Weight of parachute => W1 = mg = 5.4kg * 9.8 m/s^2 = 52.92N down
Force of Air on parachute => A N up
Tension of string => T N down

Forces on Person:
Tension of string => T N up
Weight of person => W2 = 764.4 (found the same way as above) down

Fnet on the person = 78kg * 2.8 m/s^2 = 218.4 N = T - 764.4N
solve for T... T = 982.8N

Fnet on parachute = 5.4kg * 2.8m/s^2 = 15.12N = A - T - W1,
T and W1 known:
15.12N = A - 982.8N - 52.92N
solve for A... A = answer to question (a) air resistance = 1050.84N
and the tension, T, in the string, plus the weight of the person, W2 is the answer to (b) The total downward force on the parachute is 1747.2 N.
This, however, is not the right answer...
Any help is really appreciated!
Thanks

A_lilah said:

Homework Statement

A 78 kg person is parachuting and experiencing a downward acceleration of 2.8 m/s2. The mass of the parachute is 5.4 kg.
(a) What upward force is exerted on the open parachute by the air?
(b) What downward force is exerted by the person on the parachute?

Fnet = ma

The Attempt at a Solution

Forces on parachute:
Weight of parachute => W1 = mg = 5.4kg * 9.8 m/s^2 = 52.92N down
Force of Air on parachute => A N up
Tension of string => T N down

Forces on Person:
Tension of string => T N up
Weight of person => W2 = 764.4 (found the same way as above) down

Fnet on the person = 78kg * 2.8 m/s^2 = 218.4 N = T - 764.4N
solve for T... T = 982.8N

Fnet on parachute = 5.4kg * 2.8m/s^2 = 15.12N = A - T - W1,
T and W1 known:
15.12N = A - 982.8N - 52.92N
solve for A... A = answer to question (a) air resistance = 1050.84N
and the tension, T, in the string, plus the weight of the person, W2 is the answer to (b) The total downward force on the parachute is 1747.2 N.
This, however, is not the right answer...
Any help is really appreciated!
Thanks
You've got your plus and minus signs mixed up. The net force must be in the direction of the acceleration. For the person, for example, his weight must be greater than T, in order for him to accelerate downwards.

Thank you!

1. How do you calculate the forces on a parachute and person?

To calculate the forces on a parachute and person, you will need to know the weight of the person, the surface area of the parachute, and the air resistance (drag) coefficient of the parachute. You can then use the formula F = (0.5 x p x v2 x A x Cd), where F is the drag force, p is the air density, v is the velocity, A is the surface area, and Cd is the drag coefficient. This will give you the total force acting on the parachute and person.

2. What factors affect the forces on a parachute and person?

The main factors that affect the forces on a parachute and person are the weight of the person, the surface area of the parachute, and the air resistance (drag) coefficient of the parachute. Other factors that may also play a role include the air density, the altitude, and the wind speed and direction.

3. How does the size of the parachute affect the forces?

The size of the parachute has a direct impact on the forces acting on it. A larger parachute will have a larger surface area, which will result in a higher drag force. This means that a larger parachute will experience more air resistance and therefore, a slower descent. On the other hand, a smaller parachute will have a smaller surface area and will experience less air resistance, resulting in a faster descent.

4. What is the importance of calculating the forces on a parachute and person?

Calculating the forces on a parachute and person is important for understanding the physics behind the descent of a parachute and ensuring the safety of the person using it. By knowing the forces acting on the parachute and person, we can determine the appropriate size and design of the parachute to ensure a safe and controlled descent.

5. Can you explain the concept of terminal velocity in relation to parachute descent?

Terminal velocity is the maximum speed that an object can reach while falling through a fluid, such as air. As an object falls, the force of gravity pulls it downwards, while the force of air resistance (drag) increases as the object's speed increases. At a certain point, the two forces become equal, and the object stops accelerating, reaching a constant speed known as terminal velocity. In the case of a parachute descent, the parachute and person will reach terminal velocity when the drag force of the parachute equals the weight of the person. This is important to consider when designing a parachute to ensure a safe and controlled descent.

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