Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find the normal force acting on the barrel, we need to consider the various forces involved. These forces include the gravitational force (weight) acting downward, the vertical component of the applied force acting upward, and the resulting normal force.
Here is a step-by-step breakdown:
1. Calculate the weight of the barrel:
The weight ([tex]\( W \)[/tex]) of the barrel can be calculated using the formula:
[tex]\[ W = m \cdot g \][/tex]
where [tex]\( m \)[/tex] is the mass of the barrel and [tex]\( g \)[/tex] is the acceleration due to gravity ([tex]\( 9.81 \, m/s^2 \)[/tex]).
Substituting the given values:
[tex]\[ W = 14.5 \, \text{kg} \times 9.81 \, m/s^2 = 142.245 \, \text{N} \][/tex]
2. Calculate the vertical component of the applied force:
The vertical component of the applied force ([tex]\( F_{\text{vertical}} \)[/tex]) can be found using the sine of the given angle ([tex]\( \theta \)[/tex]):
[tex]\[ F_{\text{vertical}} = F \cdot \sin(\theta) \][/tex]
where [tex]\( F \)[/tex] is the magnitude of the applied force and [tex]\( \theta \)[/tex] is the angle in degrees.
First, convert the angle from degrees to radians:
[tex]\[ \theta_{\text{radians}} = \frac{48.7^\circ \times \pi}{180} = 0.849975 \, \text{radians} \][/tex]
Now, calculate the vertical component:
[tex]\[ F_{\text{vertical}} = 22.1 \, \text{N} \cdot \sin(0.849975) = 16.6029 \, \text{N} \][/tex]
3. Calculate the normal force:
The normal force ([tex]\( N \)[/tex]) is the force exerted by the ground on the barrel that counteracts the weight and the vertical component of the applied force:
[tex]\[ N = W - F_{\text{vertical}} \][/tex]
Substituting the calculated values:
[tex]\[ N = 142.245 \, \text{N} - 16.6029 \, \text{N} = 125.642 \, \text{N} \][/tex]
Therefore, the normal force acting upon the barrel is [tex]\(\boxed{125.642 \, \text{N}}\)[/tex].
Here is a step-by-step breakdown:
1. Calculate the weight of the barrel:
The weight ([tex]\( W \)[/tex]) of the barrel can be calculated using the formula:
[tex]\[ W = m \cdot g \][/tex]
where [tex]\( m \)[/tex] is the mass of the barrel and [tex]\( g \)[/tex] is the acceleration due to gravity ([tex]\( 9.81 \, m/s^2 \)[/tex]).
Substituting the given values:
[tex]\[ W = 14.5 \, \text{kg} \times 9.81 \, m/s^2 = 142.245 \, \text{N} \][/tex]
2. Calculate the vertical component of the applied force:
The vertical component of the applied force ([tex]\( F_{\text{vertical}} \)[/tex]) can be found using the sine of the given angle ([tex]\( \theta \)[/tex]):
[tex]\[ F_{\text{vertical}} = F \cdot \sin(\theta) \][/tex]
where [tex]\( F \)[/tex] is the magnitude of the applied force and [tex]\( \theta \)[/tex] is the angle in degrees.
First, convert the angle from degrees to radians:
[tex]\[ \theta_{\text{radians}} = \frac{48.7^\circ \times \pi}{180} = 0.849975 \, \text{radians} \][/tex]
Now, calculate the vertical component:
[tex]\[ F_{\text{vertical}} = 22.1 \, \text{N} \cdot \sin(0.849975) = 16.6029 \, \text{N} \][/tex]
3. Calculate the normal force:
The normal force ([tex]\( N \)[/tex]) is the force exerted by the ground on the barrel that counteracts the weight and the vertical component of the applied force:
[tex]\[ N = W - F_{\text{vertical}} \][/tex]
Substituting the calculated values:
[tex]\[ N = 142.245 \, \text{N} - 16.6029 \, \text{N} = 125.642 \, \text{N} \][/tex]
Therefore, the normal force acting upon the barrel is [tex]\(\boxed{125.642 \, \text{N}}\)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.