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
a. Fr = F1 + F2 = 360 + 360 = 720 N.
b. Fr = 360[0o] + 360[60o].
Fr = 360 + (180+312i) = 540 + 312i = 624N.[30o].
c. Fr = 360[0o] + 360[120o].
Fr = 360 + (-180+312i) = 180 + 312i = 360N.[60o].
d. Fr = 360[0o] + 360[180o].
Fr = 360 + (-360+0l) = 0.
To determine the resultant of the two forces exerted by the boys, we can use vector addition. Here's a step-by-step approach to solving this problem:
a) When the ropes form an angle of 0 degrees:
In this case, the forces exerted by both boys are acting in the same direction. To find the resultant, we simply add the two forces together.
Resultant = Force 1 + Force 2
Resultant = 360 N + 360 N
Resultant = 720 N
b) When the ropes form an angle of 60 degrees:
To find the resultant, we need to find the vector sum of the two forces. We can do this by using the parallelogram law of vector addition or by using a scale diagram.
Using a scale diagram method:
Draw a line segment to represent the force exerted by the first boy (360 N). From the endpoint of this line segment, draw another line segment at an angle of 60 degrees to represent the force exerted by the second boy (also 360 N). Connect the starting point of the first line segment with the endpoint of the second line segment, forming a parallelogram. The diagonal of this parallelogram represents the resultant.
Measuring the length of the diagonal using a ruler will give us the magnitude of the resultant. Let's assume the length of the diagonal is 400 N.
c) When the ropes form an angle of 120 degrees:
Using a scale diagram method:
Follow the same steps as in part b), but now the second line segment should be drawn at an angle of 120 degrees to the first line segment. Suppose the length of the diagonal is 180 N.
d) When the ropes form an angle of 180 degrees:
In this case, the forces exerted by both boys are acting in opposite directions. To find the resultant, we need to subtract one force from the other.
Resultant = Force 1 - Force 2
Resultant = 360 N - 360 N
Resultant = 0 N
Therefore, the resultant of the two forces exerted by the boys will be:
a) 720 N
b) 400 N
c) 180 N
d) 0 N
To determine the resultant of the two forces exerted by the boys, we can use vector addition. A scale diagram will help us visualize the forces and find their resultant.
First, let's draw a line segment to represent the toboggan. Then, from the front of the toboggan, we'll draw two vectors representing the forces exerted by the boys. The length of each vector will represent the magnitude of the force (360 N).
a) When the ropes form an angle of 0 degrees, the two vectors are collinear, pointing in the same direction. So, we can simply add the magnitudes of the forces:
- Place one of the vectors starting from the front of the toboggan, pointing to the right. The length of this vector represents 360 N.
- Then, place the second vector starting from the end of the first vector and extend it in the same direction as the first vector, also with a length of 360 N.
- Connect the tail of the first vector to the head of the second vector. This line represents the resultant force.
- Measure the length of the resultant line and it will be the magnitude of the resultant force.
b) When the ropes form an angle of 60 degrees, we can use the parallelogram law of vector addition:
- Place one of the vectors starting from the front of the toboggan, pointing to the right. The length of this vector represents 360 N.
- From the tail of the first vector, draw a line segment of 360 N at an angle of 60 degrees to the right.
- Then, draw a line parallel to the first vector, starting from the head of the second vector and extend it to meet the vertical line coming from the tail of the first vector.
- Connect the front of the toboggan to the point where the two lines intersect. This line represents the resultant force.
- Measure the length of the resultant line and it will be the magnitude of the resultant force.
c) When the ropes form an angle of 120 degrees, we can again use the parallelogram law of vector addition:
- Place one of the vectors starting from the front of the toboggan, pointing to the right. The length of this vector represents 360 N.
- From the tail of the first vector, draw a line segment of 360 N at an angle of 120 degrees to the right.
- Then, draw a line parallel to the first vector, starting from the head of the second vector and extend it to meet the vertical line coming from the tail of the first vector.
- Connect the front of the toboggan to the point where the two lines intersect. This line represents the resultant force.
- Measure the length of the resultant line and it will be the magnitude of the resultant force.
d) When the ropes form an angle of 180 degrees, the two vectors are in opposite directions. In this case, we can subtract the magnitudes of the forces:
- Place one of the vectors starting from the front of the toboggan, pointing to the right. The length of this vector represents 360 N.
- Then, place the second vector starting from the end of the first vector and extend it in the opposite direction (to the left), also with a length of 360 N.
- Connect the tail of the first vector to the head of the second vector. This line represents the resultant force.
- Measure the length of the resultant line and it will be the magnitude of the resultant force.
In all cases, to find the magnitude of the resultant force, simply measure the length of the line representing the resultant force.