Two boys are pulling a girl along on a tobaggan. Each boy pulls on a rope attached to the same point on the front of the tobaggan with a force of 360 N. Using a scale diagram, determine the resultant of the two forces exerted by the boys if their ropes form each of these angles with each other:
a) 0 degrees
b) 60 degrees
c) 120 degrees
d) 180 degrees
Please show work
I can't make a scale drawing here. https://www.physicsforums.com/attachments/addvecs-jpg.87776/
is a similar sketch.
To determine the resultant of the two forces exerted by the boys, we can use the vector addition method. We will start by drawing a scale diagram.
a) When the ropes form an angle of 0 degrees:
In this case, the two forces are acting in the same direction, so the resultant will be the algebraic sum of the two forces.
Draw a line segment to represent the force exerted by the first boy. Label it as 360 N.
Draw a line segment next to it to represent the force exerted by the second boy. Label it as 360 N.
Extend the line segments to form a parallelogram.
Measure the length of the diagonal formed from the starting point of the first boy's force to the ending point of the second boy's force.
The length of the diagonal represents the magnitude of the resultant force.
Measure the angle that the diagonal makes with the first boy's force.
This angle represents the direction of the resultant force.
b) When the ropes form an angle of 60 degrees:
In this case, we can use the parallelogram method or the triangle method to find the resultant vector.
Using the parallelogram method, draw a line segment to represent the force exerted by the first boy. Label it as 360 N.
Draw a line segment to represent the force exerted by the second boy. Label it as 360 N.
Starting from the endpoint of the first boy's force, draw a line segment that represents the force exerted by the second boy.
Draw a line segment from the starting point of the first boy's force to the endpoint of the second boy's force.
Measure the length of this diagonal. This length represents the magnitude of the resultant force.
Measure the angle that this diagonal makes with the first boy's force. This angle represents the direction of the resultant force.
c) When the ropes form an angle of 120 degrees:
Using the triangle method, draw a line segment to represent the force exerted by the first boy. Label it as 360 N.
Draw a line segment to represent the force exerted by the second boy. Label it as 360 N.
Starting from the endpoint of the first boy's force, draw a line segment that represents the force exerted by the second boy.
Complete the triangle by drawing a line segment from the starting point of the first boy's force to the endpoint of the second boy's force.
Measure the length of the side opposite the angle formed by the two forces. This length represents the magnitude of the resultant force.
Measure the angle formed by the two forces. This angle represents the direction of the resultant force.
d) When the ropes form an angle of 180 degrees:
In this case, the two forces are equal in magnitude but opposite in direction.
Draw a line segment to represent the force exerted by the first boy. Label it as 360 N.
Draw a line segment next to it in the opposite direction to represent the force exerted by the second boy. Label it as -360 N.
Draw a line segment from the starting point of the first boy's force to the endpoint of the second boy's force.
Measure the length of this line segment. This length represents the magnitude of the resultant force.
Measure the angle that this line segment makes with the first boy's force. This angle represents the direction of the resultant force.
Remember to use a consistent scale for your diagram to accurately measure lengths and angles.
To determine the resultant of the two forces exerted by the boys, we can use vector addition. The resultant is the vector sum of the two forces.
Let's start by drawing a scale diagram to represent the situation. Choose a suitable scale (such as 1 cm = 100 N) and draw a horizontal line to represent the toboggan. Label the point where the ropes are attached as point A.
a) When the ropes form an angle of 0 degrees with each other:
In this case, both boys are pulling the toboggan in the same direction. Draw two arrows of length 3.6 cm (since 1 cm represents 100 N) starting from point A in the same direction. These arrows represent the forces exerted by the boys.
Join the tail of the first arrow to the tip of the second arrow. The line formed represents the resultant force. Measure its length and convert it to the appropriate scale. This will be the magnitude of the resultant force.
b) When the ropes form an angle of 60 degrees with each other:
In this case, the forces create an equilateral triangle. Draw two arrows of length 3.6 cm from point A, separated by an angle of 60 degrees.
Join the tail of the first arrow to the tip of the second arrow. Measure the length of this line and convert it to the appropriate scale. This will be the magnitude of the resultant force.
c) When the ropes form an angle of 120 degrees with each other:
In this case, the forces create a scalene triangle. Draw two arrows of length 3.6 cm from point A, separated by an angle of 120 degrees.
Join the tail of the first arrow to the tip of the second arrow. Measure the length of this line and convert it to the appropriate scale. This will be the magnitude of the resultant force.
d) When the ropes form an angle of 180 degrees with each other:
In this case, the forces are in opposite directions, pulling against each other. Draw two arrows of length 3.6 cm from point A, pointing in opposite directions.
Join the tail of the first arrow to the tip of the second arrow. Measure the length of this line and convert it to the appropriate scale. This will be the magnitude of the resultant force.
After finding the magnitude of the resultant force for each case, you can indicate its direction using an arrow or by providing the angle it makes with the horizontal line.