Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30 N, and the other east and at an angle of 30° northward and a tension force of 40 N. Find the components of the net force on the cart. Show all your work.
To find the components of the net force on the wagon, we need to break down the forces into their horizontal and vertical components.
First, let's analyze the horizontal forces. The rope pulling to the west provides a force with a magnitude of 30 N in the negative x-direction. The rope pulling to the east and at an angle of 30° northward can be divided into horizontal and vertical components.
The horizontal component of the eastward force can be found by multiplying the magnitude of the force (40 N) by the cosine of the angle (30°):
Horizontal component = 40 N * cos(30°) = 40 N * 0.866 = 34.64 N
The vertical component of the eastward force can be found by multiplying the magnitude of the force (40 N) by the sine of the angle (30°):
Vertical component = 40 N * sin(30°) = 40 N * 0.5 = 20 N
Now, let's summarize the horizontal forces:
- Westward force: -30 N
- Eastward force (horizontal component): 34.64 N
The net horizontal force can be calculated by adding up these forces:
Net horizontal force = -30 N + 34.64 N = 4.64 N
Next, let's analyze the vertical forces. The vertical component of the eastward force is 20 N.
Now, let's summarize the vertical forces:
- Eastward force (vertical component): 20 N
The net vertical force can be calculated by adding up these forces:
Net vertical force = 20 N
Finally, let's summarize the components of the net force on the wagon:
- Horizontal component: 4.64 N towards the east
- Vertical component: 20 N upwards
So, the net force on the wagon has a magnitude of 4.64 N towards the east and 20 N upwards.
To find the components of the net force on the cart, we need to break down the forces into their horizontal and vertical components.
Given:
Tension force of the horizontal rope (west direction): 30 N
Tension force of the angled rope (east direction, 30° northward): 40 N
Step 1: Break down the angled rope into its horizontal and vertical components.
The given angled force (40 N) can be resolved into horizontal and vertical components using trigonometry.
Horizontal component: The horizontal component is found using the cosine function. Cosine of 30° is √3/2.
Horizontal component = Force * cos(angle)
Horizontal component = 40 N * √3/2
Horizontal component = 20√3 N
Vertical component: The vertical component is found using the sine function. Sine of 30° is 1/2.
Vertical component = Force * sin(angle)
Vertical component = 40 N * 1/2
Vertical component = 20 N
Step 2: Determine the net force components.
The net force in the horizontal direction is the difference between the horizontal forces acting in opposite directions (west and east).
Net horizontal force = Force (west) - Force (east)
Net horizontal force = 30 N - 20√3 N
The net force in the vertical direction is the sum of the vertical forces.
Net vertical force = Force (northward)
Step 3: Calculate the net force components.
Net horizontal force = 30 N - 20√3 N
Net vertical force = 20 N
So, the components of the net force on the cart are:
- Net horizontal force: 30 N - 20√3 N
- Net vertical force: 20 N
platinum resistance thermometer has a resistance of 5? at 0°and 9?
How about showing YOUR work?
Add the north components and the east components separately.
Rope 1: -30 N east, 0 north
Rope 2: 40 sin 30 north, 40 cos 30 east