2. A heavy box is pulled across a wooden floor with a rope. The rope forms an angle of 60.0°with the floor. A tension of 80.0° N maintained on the rope. What are the horizontal and vertical components of the force?
vertical: 80sin60.
horizonal: 80 cos 60
Well, isn't this a "weighty" question! Let me calculate the horizontal and vertical components of that tension for you.
Given that the tension in the rope is 80.0 N, and the angle with the floor is 60.0°, we can break down this force into its horizontal and vertical components.
The horizontal component is given by the formula T * cos(theta), where T is the tension and theta is the angle. So the horizontal component will be 80.0 N * cos(60.0°). Quick calculation time...
The horizontal component of the force is approximately 40.0 N. So, our heavy box is "pulling" with 40.0 N horizontally.
Now, let's calculate the vertical component. It is given by the formula T * sin(theta).
So, the vertical component of the force is 80.0 N * sin(60.0°). Let me grab my calculator real quick...
The vertical component of the force is approximately 69.3 N. That means the box is "lifting" with approximately 69.3 N vertically.
So, the horizontal component is 40.0 N, and the vertical component is 69.3 N. I hope that clears things up!
To find the horizontal and vertical components of the force, we can use trigonometry.
Given:
Angle of the rope with the floor: 60.0°
Tension in the rope: 80.0 N
Horizontal component of the force (Fx):
The horizontal component of the force can be calculated by using the formula:
Fx = Tension * cos(angle)
Let's substitute the given values into the formula:
Fx = 80.0 N * cos(60.0°)
Using a calculator, we can evaluate the cosine of 60.0°:
cos(60.0°) ≈ 0.5
Now we can calculate the horizontal component:
Fx = 80.0 N * 0.5
Fx = 40.0 N
Therefore, the horizontal component of the force is 40.0 N.
Vertical component of the force (Fy):
The vertical component of the force can be calculated by using the formula:
Fy = Tension * sin(angle)
Let's substitute the given values into the formula:
Fy = 80.0 N * sin(60.0°)
Using a calculator, we can evaluate the sine of 60.0°:
sin(60.0°) ≈ 0.866
Now we can calculate the vertical component:
Fy = 80.0 N * 0.866
Fy ≈ 69.28 N
Therefore, the vertical component of the force is approximately 69.28 N.
To find the horizontal and vertical components of the force, we can use trigonometry.
First, let's define the given information:
- The angle between the rope and the floor is 60.0°.
- The tension in the rope is 80.0 N.
To determine the horizontal component of the force, we use the formula:
Horizontal component = Tension * cos(angle)
Substituting the values into the formula:
Horizontal component = 80.0 N * cos(60.0°)
Using a scientific calculator, we can find that cos(60.0°) is equal to 0.5.
Horizontal component = 80.0 N * 0.5 = 40.0 N
Therefore, the horizontal component of the force is 40.0 N.
To determine the vertical component of the force, we use the formula:
Vertical component = Tension * sin(angle)
Substituting the values into the formula:
Vertical component = 80.0 N * sin(60.0°)
Using a scientific calculator, we can find that sin(60.0°) is equal to 0.866.
Vertical component = 80.0 N * 0.866 = 69.3 N
Therefore, the vertical component of the force is 69.3 N.