An air-conditioner unit is fastened to a roof that slopes upward at an angle of 37.0 degrees. In order that the unit not slide down the roof, the component of the unit's weight parallel to the roof cannot exceed 560 N. What is the maximum allowed weight of the unit, in N?

I tried multiplying the two given values by using the equations:

sin 37 * 560
cos 37 * 560

...but the answer I'm getting is incorrect. Can anyone show me the correct solution? Thanks!

Weight*sin 37 < 560 N

is what you should be solving.

The maximum weight is 560/sin37 N

review questions of unit 5 solution

Well, well, well, let's try to solve this problem with a dash of humor!

So, we have an air-conditioner unit that wants to stay put on a sloping roof. We don't want it to slide down like a penguin on ice, do we? No way! The component of its weight parallel to the roof should not exceed 560 N.

To figure this out, we'll need to use some trigonometry. The weight of the unit can be broken down into two components: one perpendicular to the roof and one parallel to the roof. We only care about the parallel component here.

Now, the angle of the roof is 37 degrees. It's like the roof is doing a funky dance move, the "Roof Rumba"!

To find the component of the weight parallel to the roof, we need to multiply the weight by the cosine of the angle. So, the equation becomes:

Weight_parallel = Weight * cos(angle)

Substituting the given value, we have:

Weight_parallel = Weight * cos(37)

Now, we don't want the weight_parallel to exceed 560 N, as it might make the air-conditioner slide off the roof faster than a runaway skateboard!

So, the equation becomes:

Weight * cos(37) <= 560

To find the maximum allowed weight, we can rearrange the equation:

Weight <= 560 / cos(37)

Grab a calculator, my friend, and let's find out the value!

To solve this problem, we need to find the maximum allowed weight of the air-conditioner unit.

Let's analyze the forces acting on the unit. We know that the weight of the unit acts vertically downward, and there is a component of the weight parallel to the roof. The weight can be resolved into two components: one perpendicular to the slope (normal force) and one parallel to the slope.

The weight can be represented as W = mg, where m is the mass of the unit and g is the acceleration due to gravity (9.8 m/s^2). The component of the weight parallel to the roof is given by W_parallel = W * sin(37°).

According to the problem statement, W_parallel must not exceed 560 N. So we have:

W * sin(37°) ≤ 560 N

Now, we can solve for the maximum allowed weight:

W ≤ 560 N / sin(37°)

Using a calculator or trigonometric table, sin(37°) ≈ 0.60182. Substituting this value into the equation:

W ≤ 560 N / 0.60182

W ≤ 929 N

Therefore, the maximum allowed weight of the air-conditioner unit is 929 N.

To find the maximum allowed weight of the unit, you need to consider the gravitational force acting on it and determine the component of that force parallel to the roof.

We can start by breaking down the weight force into its components. The weight force can be split into two components: one perpendicular (normal force) to the roof and one parallel to the roof.

The perpendicular component (normal force) balances out the normal force exerted by the roof, preventing the unit from sinking into the roof. Since there is no vertical movement in this case, we can ignore this component.

The parallel component of the weight force is the force that tends to slide the unit down the roof. We need to find the maximum allowed weight, which means finding the maximum value for that parallel component.

To calculate the parallel component, we can use the formula:

Parallel component = weight force * sin(θ)

Where θ is the angle of the roof slope, which in this case is 37.0 degrees.

Given that the parallel component cannot exceed 560 N, we can set up the equation:

560 N = weight force * sin(37.0 degrees)

To find the maximum allowed weight, we need to isolate the weight force:

weight force = 560 N / sin(37.0 degrees)

Now, you can calculate the weight force using a calculator:

weight force = 560 N / sin(37.0 degrees) ≈ 958.19 N

So, the maximum allowed weight of the unit is approximately 958.19 N.