In the figure the man hanging upside down is holding a partner who weighs 535 N. Assume
that the partner moves on a circle that has a radius of 6.50 m. At a swinging speed of 3.75 m/s,
what force must the man apply 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 can use the concept of centripetal force.
The centripetal force is the force that keeps an object moving in a circular path and is given by the formula:
F = (m * v^2) / r
Where:
- F is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circular path
In this case, the mass of the partner is not given directly, but we are provided with the weight, which is 535 N. The weight of an object is given by the formula:
W = m * g
Where:
- W is the weight
- m is the mass
- g is the acceleration due to gravity
Since we know the weight, we can find the mass of the partner using the formula:
m = W / g
Now we can determine the mass of the partner:
m = 535 N / 9.8 m/s^2
m ≈ 54.6 kg
Now we can substitute the values into the centripetal force formula:
F = (m * v^2) / r
F = (54.6 kg * (3.75 m/s)^2) / 6.5 m
F ≈ 74.85 N
Therefore, the man must apply a force of approximately 74.85 N to his partner in the straight-down position.