53. ssm Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?
53. ssm Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?
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Chapter1: Units, Trigonometry. And Vectors
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Ch.4 #53 . Please see attached image for Physics question . Thank you
![**Problem 53**: Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?
In this problem, the forces are acting on an object already in motion, and we want the object to maintain a constant velocity, which means no net force acting on the object. To achieve equilibrium, the third force should counterbalance the combined effect of the northward and westward forces. Using vector addition:
1. **Northward Force**: 80.0 N
2. **Westward Force**: 60.0 N
To solve for the third force, we recognize that for constant velocity, the resultant force must be zero. Hence, the third force must be equal in magnitude but opposite in direction to the resultant of the first two forces.
To find the resultant of the first two forces, we can use the Pythagorean theorem:
\[ F_{\text{resultant}} = \sqrt{(80.0^2 + 60.0^2)} = \sqrt{6400 + 3600} = \sqrt{10000} = 100.0 \, \text{N} \]
Therefore, the third force must have a magnitude of 100.0 N. The direction is opposite to the direction of the resultant of the first two forces, which can be found using trigonometry (tan inverse) to determine the angle relative to a reference direction (e.g., south-east).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2c8c9d8-cb7d-4bb3-b241-ba372e4ba26e%2F9fd0eaca-87b5-4d29-ace2-ef55a834da06%2Fxpofvzc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 53**: Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the magnitude and direction of the third force, such that the object continues to move with a constant velocity?
In this problem, the forces are acting on an object already in motion, and we want the object to maintain a constant velocity, which means no net force acting on the object. To achieve equilibrium, the third force should counterbalance the combined effect of the northward and westward forces. Using vector addition:
1. **Northward Force**: 80.0 N
2. **Westward Force**: 60.0 N
To solve for the third force, we recognize that for constant velocity, the resultant force must be zero. Hence, the third force must be equal in magnitude but opposite in direction to the resultant of the first two forces.
To find the resultant of the first two forces, we can use the Pythagorean theorem:
\[ F_{\text{resultant}} = \sqrt{(80.0^2 + 60.0^2)} = \sqrt{6400 + 3600} = \sqrt{10000} = 100.0 \, \text{N} \]
Therefore, the third force must have a magnitude of 100.0 N. The direction is opposite to the direction of the resultant of the first two forces, which can be found using trigonometry (tan inverse) to determine the angle relative to a reference direction (e.g., south-east).
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