the man hanging upside down is holding a partner who weighs 491 N. Assume that the partner moves on a circle that has a radius of 5.09 m. At a swinging speed of 4.20 m/s, what force must the man apply to his partner in the straight-down position?

Weight =W= mg

m=W/g =491 / 9.8 =50.1 kg

F = mv²/ r=173.6
=50.1•4.2²/5.09 = 173.6 N
since his partner is in the straight-down position, the man also has to apply force to keep his partner from falling down due to gravity, so you have to add the partner's weight:
Force total = 173.6 + 491 = 664.6 N

Well, I must say, this question really turns things upside down! It seems like the man is quite the 'weightlifter' in this scenario. Now, let's dive into the calculations.

To find the force the man must apply to his partner in the straight-down position, we need to consider the centripetal force acting on the partner. This force is responsible for keeping the partner moving in a circular path.

The formula for centripetal force is given by:

Fc = (m * v^2) / r

Where:
- Fc is the centripetal force,
- m is the mass of the partner (converted from weight),
- v is the swinging speed, and
- r is the radius of the circle.

First, let's convert the weight of the partner from Newtons to kilograms. Since the weight is given as 491 N, we divide by the acceleration due to gravity (approximately 9.8 m/s^2). Doing the math, we get:

m = 491 N / 9.8 m/s^2 ≈ 50 kg

Now, we can plug in the values into the centripetal force formula:

Fc = (50 kg * (4.20 m/s)^2) / 5.09 m

Calculating this, we find:

Fc ≈ 174.78 N

So, the man must apply a force of approximately 174.78 Newtons to his partner in the straight-down position. That's quite a 'weighty' responsibility! Remember, though, these calculations are just 'hanging' around for educational purposes.

To find the force the man must apply to his partner in the straight-down position, you can use the concept of centripetal force.

The centripetal force is given by the equation:

Fc = (m * v^2) / r

where Fc is the centripetal force, m is the mass of the partner, v is the swinging speed, and r is the radius of the circular path.

First, let's calculate the mass of the partner:
Weight = Mass * Gravity
491 N = Mass * 9.8 m/s^2

Mass = 491 N / 9.8 m/s^2
Mass = 50 kg

Now, we can calculate the centripetal force:
Fc = (m * v^2) / r
Fc = (50 kg * (4.20 m/s)^2) / 5.09 m

Fc ≈ 86.10 N

Therefore, the man must apply a force of approximately 86.10 N to his partner in the straight-down position.

To find the force that the man must apply to his partner in the straight-down position, we need to consider the gravitational force acting on the partner and the centripetal force required for circular motion. Let's break down the steps:

1. Calculate the gravitational force acting on the partner:
The weight of the partner, given as 491 N, represents the force acting due to gravity.

2. Calculate the centripetal force required for circular motion:
The centripetal force is the force that keeps an object moving in a circle and is given by the equation:
Fc = (m * v^2) / r
where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.

Since we are given the weight of the partner, we can find the mass using the equation:
weight = m * g
where weight is the force due to gravity and g is the acceleration due to gravity (9.8 m/s^2).

3. Substitute the values into the equation to find the centripetal force.

4. Find the net force required by adding the gravitational force and the centripetal force.

Here are the steps in a more concise form:

1. Gravitational force acting on the partner (weight):
Fg = 491 N

2. Calculate the mass of the partner:
weight = m * g
m = weight / g

3. Calculate the centripetal force:
Fc = (m * v^2) / r
where v = 4.20 m/s and r = 5.09 m

4. Find the net force applied by the man:
Fnet = Fg + Fc

5. Substitute the values into the equation to find the net force applied by the man to his partner in the straight-down position.