A 105-N suitcase sits on a rubber ramp at an airport carousel at a 25 degree angle . The weight vector can be broken into two perpendicular components. What is the magnitude of the component parallel to the ramp surface?
105 sin25 (N)
To find the magnitude of the component parallel to the ramp surface, we need to break down the weight vector into its components.
Given:
Weight of the suitcase (W) = 105 N
Angle of the ramp (θ) = 25 degrees
We can start by finding the component parallel to the ramp surface (W_parallel). We can use the equation:
W_parallel = W * sin(θ)
Let's calculate it step by step:
1. Convert the angle from degrees to radians:
θ_radians = θ * (π/180)
θ_radians = 25 * (π/180)
θ_radians ≈ 0.436 radians
2. Substitute the values into the equation:
W_parallel = 105 * sin(0.436)
3. Calculate the sine of the angle:
sin(0.436) ≈ 0.4226
4. Multiply the weight by the sine of the angle:
W_parallel ≈ 105 * 0.4226
W_parallel ≈ 44.36 N
Therefore, the magnitude of the component parallel to the ramp surface is approximately 44.36 N.
To find the magnitude of the component of the weight vector parallel to the ramp surface, we need to determine the force acting in that direction. This can be done by calculating the horizontal component of the weight vector.
The weight vector can be broken into two perpendicular components: one parallel to the ramp surface and one perpendicular to the ramp surface. The component parallel to the ramp surface is the horizontal component.
To calculate the horizontal component, we need to use trigonometry. The weight vector can be represented as the hypotenuse of a right triangle. The angle formed between the weight vector and the ramp surface is given as 25 degrees.
Using the given information, we can use the trigonometric function cosine (cos) to find the horizontal component:
Horizontal component = Weight vector * cos(angle)
The weight vector is given as 105 N, and the angle is 25 degrees. Plugging these values into the equation, we get:
Horizontal component = 105 N * cos(25 degrees)
Using a scientific calculator or a calculator with trigonometric functions, find the cosine of 25 degrees:
cos(25 degrees) ≈ 0.90631
Now, substitute this value back into the equation:
Horizontal component = 105 N * 0.90631
Multiply these two values together to find the magnitude of the component parallel to the ramp surface:
Horizontal component ≈ 95.16455 N
Therefore, the magnitude of the component parallel to the ramp surface is approximately 95.16455 N.