pete and john play a game of tug war on a frictionless icy curface. pete weighs 539 N and john weights 392 N. during the course of the game, john accelerates toward pete at a rate of 3 m/s^2. Sarah decideds to join the game as well. Now pete pulls on Sarah with a force of 45.0N [E] and john pulls on her with a force of 25N [N]. What's Sarah's resultant acceleration, if she weighs 294 N?
m=294N (this equals 30kg)
Fjohn=25 N [N]
Fpete=45 N [E]
Fnet=Fjohn+Fpete
=25^2 + 45^2
=51N
a=F/m
=51/30kg
=1.7m/s^2
Now, Im just confused about what angle to solve for. My diagram looks like this: have an arrowed line going west, to represent Pete and then from that arrow's head, I have an arrow going North to represent John. If this is correct, then I would solve for Tan, with the opposide side=25N and the the adjacent side equaling 45N, to give an angle of 29degrees. Is this correcct?
In order to determine the resultant acceleration of Sarah, we need to consider the forces acting on her and their directions.
Pete is pulling with a force of 45.0 N in the east direction, while John is pulling with a force of 25.0 N in the north direction.
To find the resultant force, we can use vector addition. We will split each force into its horizontal and vertical components.
The horizontal component of Pete's force is 45.0 N and the vertical component is 0 N.
The horizontal component of John's force is 0 N and the vertical component is 25.0 N.
Now we can add the horizontal and vertical components separately.
Horizontal component: 45.0 N + 0 N = 45.0 N
Vertical component: 0 N + 25.0 N = 25.0 N
We now have the horizontal and vertical components of the resultant force.
To find the magnitude and direction of the resultant force, we can use the Pythagorean theorem.
Magnitude of the resultant force:
√ (45.0 N)^2 + (25.0 N)^2 = √ (2025 N^2 + 625 N^2) = √ (2650 N^2) = 51.48 N (approx)
To find the direction of the resultant force, we can use trigonometry.
Tangent of the angle:
tanθ = (opposite side / adjacent side) = (25.0 N / 45.0 N) = 0.556
To find the angle θ, we take the inverse tangent (tan^-1) of 0.556:
θ = tan^-1(0.556) = 29.81 degrees (approx)
Therefore, Sarah's resultant acceleration is approximately 51.48 N directed at an angle of 29.81 degrees north of east.
Yes, your diagram is correct. To solve for the angle, you can use the tangent function as you mentioned. The opposite side is 25N and the adjacent side is 45N. So you can calculate the angle using the formula:
tan(angle) = opposite/adjacent
tan(angle) = 25/45
To find the angle, you can use the inverse tangent function:
angle = atan(25/45)
angle ≈ 29.03 degrees
So the angle between John's force and Pete's force is approximately 29.03 degrees.