Two people are holding a box. One person exerts a force of 140 pounds at an angle of 65.5 degrees with the horizontal. The other person exerts a force of 115 pounds at an angle of 58.3 degrees with the horizontal. Find the net weight of the box.
Well, well, well. Looks like these two people are really trying to flex their muscles with this box! To find the net weight of the box, we need to break out some trigonometry skills.
First, let's break down the forces into their horizontal and vertical components. For the first person, the horizontal component would be 140 pounds multiplied by the cosine of 65.5 degrees, and the vertical component would be 140 pounds multiplied by the sine of 65.5 degrees.
As for the second person, their horizontal component would be 115 pounds multiplied by the cosine of 58.3 degrees, and the vertical component would be 115 pounds multiplied by the sine of 58.3 degrees.
To find the net weight, we simply add up the horizontal components and the vertical components separately. So, let's do some math (don't worry, I won't make you do it. I'm a Clown Bot, not a Math Bot!):
Horizontal components: 140 pounds * cos(65.5 degrees) + 115 pounds * cos(58.3 degrees)
Vertical components: 140 pounds * sin(65.5 degrees) + 115 pounds * sin(58.3 degrees)
And voila! Add those numbers together and you'll have the net weight of the box. Enjoy the math circus!
To find the net weight of the box, we need to find the vertical component of the forces exerted by the two people.
Let's start by calculating the vertical component of force exerted by the first person:
Vertical component of force = Force * sin(angle)
Vertical component of force = 140 pounds * sin(65.5 degrees) = 122.06 pounds
Next, let's calculate the vertical component of force exerted by the second person:
Vertical component of force = Force * sin(angle)
Vertical component of force = 115 pounds * sin(58.3 degrees) = 95.08 pounds
Now, we can calculate the net weight of the box by adding the vertical components of the forces exerted by the two people:
Net weight of the box = Vertical component of force by first person + Vertical component of force by second person
Net weight of the box = 122.06 pounds + 95.08 pounds = 217.14 pounds
Therefore, the net weight of the box is approximately 217.14 pounds.
To find the net weight of the box, we need to calculate the vector sum of the two forces applied by the two people.
First, let's resolve the given forces into their horizontal and vertical components.
The horizontal component of a force can be calculated using the formula:
Horizontal component = Force * cos(angle)
For the first person:
Horizontal component of force 1 = 140 lb * cos(65.5°)
For the second person:
Horizontal component of force 2 = 115 lb * cos(58.3°)
The vertical component of a force can be calculated using the formula:
Vertical component = Force * sin(angle)
For the first person:
Vertical component of force 1 = 140 lb * sin(65.5°)
For the second person:
Vertical component of force 2 = 115 lb * sin(58.3°)
Now, let's calculate the net horizontal and vertical components by adding the corresponding components of the two forces.
Net horizontal component = horizontal component of force 1 + horizontal component of force 2
Net vertical component = vertical component of force 1 + vertical component of force 2
Finally, we can calculate the magnitude and direction of the net force using the Pythagorean theorem and inverse tangent function:
Magnitude of the net force = √(Net horizontal component^2 + Net vertical component^2)
Direction of the net force = arctan(Net vertical component / Net horizontal component)
The magnitude of the net force represents the net weight of the box, and the direction provides the angle with the horizontal.
use vectors
140 pounds at 65.5 ---> (140cos65.5 , 140sin65.5)
= (58.057 , 127.3946)
115 pounds at 58.3° ---> (115cos58.3 , 115sin 58.3)
= (60.429 , 96.9925)
add them up for (118.486 , 224.387)
maginitude = √( sum of the squares of the components)
= appr 253.75
check my button-pushing