A crate is pulled to the right with a force

of 85.5 N, to the left with a force of 120.8 N,
upward with a force of 652.1 N, and downward
with a force of 249.5 N.
What is the net external force in the x
direction?
Answer in units of N.
What is the net external force in the y direc-
tion?
Answer in units of N.
What is the magnitude of the net external
force on the crate?
Answer in units of N.
What is the direction of the net external force
on the crate (as an angle between −180� and
180�, measured from the positive x axis with
counterclockwise positive)?
Answer in units of �.

6 N

To find the net external force in the x direction, we need to calculate the sum of all the forces acting in the x direction.

Given:
Force to the right = 85.5 N
Force to the left = 120.8 N

Net external force in x direction = Force to the right - Force to the left
= 85.5 N - 120.8 N

To find the net external force in the y direction, we need to calculate the sum of all the forces acting in the y direction.

Given:
Force upward = 652.1 N
Force downward = 249.5 N

Net external force in y direction = Force upward - Force downward
= 652.1 N - 249.5 N

To find the magnitude of the net external force on the crate, we can use the Pythagorean theorem as follows:

Magnitude of net external force = sqrt((net external force in x direction)^2 + (net external force in y direction)^2)

To find the direction of the net external force on the crate, we can use trigonometry. The direction is determined by the angle between the positive x-axis and the net external force vector. We can calculate this angle using the arctan function:

Direction of net external force = arctan(net external force in y direction / net external force in x direction)

Let's calculate the answers step by step:

Net external force in the x direction:
Net external force in x direction = 85.5 N - 120.8 N
= -35.3 N (to the left)

Net external force in the y direction:
Net external force in y direction = 652.1 N - 249.5 N
= 402.6 N (upward)

Magnitude of the net external force on the crate:
Magnitude of net external force = sqrt((-35.3 N)^2 + (402.6 N)^2)
= sqrt(1249.09 N^2 + 162104.76 N^2)
= sqrt(163353.85 N^2)
= 404.15 N

Direction of the net external force on the crate:
Direction of net external force = arctan(402.6 N / -35.3 N)
= arctan(-11.4)
≈ -84.9 degrees (measured counterclockwise from the positive x-axis)

So the answers are:
Net external force in the x direction: -35.3 N (leftward)
Net external force in the y direction: 402.6 N (upward)
Magnitude of the net external force on the crate: 404.15 N
Direction of the net external force on the crate: -84.9 degrees

To find the net external force in the x-direction, we need to calculate the vector sum of the forces acting in the x-direction.

The given forces are:
Force to the right (x-direction): 85.5 N
Force to the left (x-direction): 120.8 N

The net external force in the x-direction can be found by subtracting the force to the left from the force to the right:
Net external force in x-direction = Force to the right - Force to the left
= 85.5 N - 120.8 N

Now let's calculate the net external force in the x-direction:
Net external force in x-direction = -35.3 N (since the force to the left is greater)

To find the net external force in the y-direction, we need to calculate the vector sum of the forces acting in the y-direction.

The given forces are:
Force upward (y-direction): 652.1 N
Force downward (y-direction): 249.5 N

The net external force in the y-direction can be found by subtracting the force downward from the force upward:
Net external force in y-direction = Force upward - Force downward
= 652.1 N - 249.5 N

Now let's calculate the net external force in the y-direction:
Net external force in y-direction = 402.6 N (since the force upward is greater)

To find the magnitude of the net external force on the crate, we can use the Pythagorean theorem.

Magnitude of the net external force = √[(Net external force in x-direction)^2 + (Net external force in y-direction)^2]
= √[(-35.3 N)^2 + (402.6 N)^2]

Now let's calculate the magnitude of the net external force:
Magnitude of the net external force = 407.7 N

To find the direction of the net external force on the crate, we can use trigonometry.

Direction of the net external force = atan(Net external force in y-direction / Net external force in x-direction)
= atan(402.6 N / -35.3 N)

Now let's calculate the direction of the net external force:
Direction of the net external force = -83.23 degrees (rounded to two decimal places)

So, the answers to the provided questions are:
Net external force in the x-direction: -35.3 N
Net external force in the y-direction: 402.6 N
Magnitude of the net external force on the crate: 407.7 N
Direction of the net external force on the crate: -83.23 degrees