A warehouse worker pushes a crate along the floor, as shown in the figure , by a force of 10.0 N that points downward at an angle of 45.0 degree below the horizontal.
A. Find the horizontal component of the push.
B.Find the vertical component of the push.
Horizontal (x)=Fcos(a)
10N(cos(45))=7.07
Vertical (y)=Fsin (a)
10N(sin(45))=7.07
A. Why did the push go for a horizontal component? It didn't even bring snacks! It must be thinking, "I'm done with vertical, time to go horizontal!" But seriously, to find the horizontal component of the push, you can use a little trigonometry. The force applied can be divided into its horizontal and vertical components. Since the angle is given as 45.0 degrees below the horizontal, we need to find the horizontal component. Using cosine, we can say that the horizontal component equals the force times the cosine of the angle:
Horizontal component = 10.0 N * cos(45.0 degrees)
B. Now let's find the vertical component of the push. This component will make the crate go up or down. It's like giving the crate a high five in the vertical direction. To calculate it, we can use another dose of trigonometry. The vertical component equals the force times the sine of the angle:
Vertical component = 10.0 N * sin(45.0 degrees)
Remember, these formulas are no joke, unless you're a math clown!
A. To find the horizontal component of the push, we need to find the cosine of the angle. The horizontal component can be calculated using the formula:
Horizontal component = Force × cos(angle)
Given:
Force = 10.0 N
Angle = 45.0 degrees
Plugging the values into the formula, we have:
Horizontal component = 10.0 N × cos(45.0 degrees)
Using a scientific calculator, cos(45.0 degrees) = 0.707
Horizontal component = 10.0 N × 0.707
Horizontal component = 7.07 N
Therefore, the horizontal component of the push is 7.07 N.
B. To find the vertical component of the push, we need to find the sine of the angle. The vertical component can be calculated using the formula:
Vertical component = Force × sin(angle)
Given:
Force = 10.0 N
Angle = 45.0 degrees
Plugging the values into the formula, we have:
Vertical component = 10.0 N × sin(45.0 degrees)
Using a scientific calculator, sin(45.0 degrees) = 0.707
Vertical component = 10.0 N × 0.707
Vertical component = 7.07 N
Therefore, the vertical component of the push is 7.07 N.
To find the horizontal and vertical components of the push force, we can use trigonometry.
A. The horizontal component of the push force can be found using the formula: horizontal component = force * cos(angle)
Given that the force = 10.0 N and the angle = 45.0 degrees, we can calculate the horizontal component as follows:
Horizontal component = 10.0 N * cos(45.0 degrees)
= 10.0 N * 0.7071
= 7.071 N
Therefore, the horizontal component of the push force is 7.071 N.
B. The vertical component of the push force can be found using the formula: vertical component = force * sin(angle)
Given that the force = 10.0 N and the angle = 45.0 degrees, we can calculate the vertical component as follows:
Vertical component = 10.0 N * sin(45.0 degrees)
= 10.0 N * 0.7071
= 7.071 N
Therefore, the vertical component of the push force is 7.071 N.