Part 1Two forces of 3333 N (newtons) and 5050 N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force. Part 1The magnitude of the resultant is [input]enter your response here Newtons.(Round to the nearest integer as needed.)Part 2The angle the resultant makes with the smaller force is [input]enter your response here degrees°.(Round to the nearest integer as needed.)

Question

Part 1Two forces of 3333 N​ (newtons) and 5050 N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force. Part 1The magnitude of the resultant is [input]enter your response here Newtons.​(Round to the nearest integer as​ needed.)Part 2The angle the resultant makes with the smaller force is [input]enter your response here degrees°.​(Round to the nearest integer as​ needed.)

BlackTom AI · Accepted Answer

Question restatement:
Two forces, 3333 N and 5050 N, act on an object at right angles. Part 1 asks for the magnitude of the resultant force, rounded to the nearest integer (in Newtons). Part 2 asks for the angle that the resultant makes with the smaller force, rounded to the nearest integer (in degrees).

Step-by-step analysis of each option (even though no multiple-choice options are provided, we treat the two requested quantities separately):

1) Magnitude of the resultant
- Since the forces are perpendicular, use the Pythagorean sum: R = sqrt(F1^2 + F2^2).
- Compute squares carefully:
  - 3333^2 = 11,108,889
  - 5050^2 = 25,502,500
- Add them: 11,108,889 + 25,502,500 = 36,611,389.
- Take the square root to find the magnitude: sqrt(36,611,389) ≈ 6050.9 (approximately 6051 when rounded to the nearest whole number).
- Rounding to the nearest integer yields about 6051 N. If someone arrives at 6034 N, that value would be notably off because it implies a smaller resultant than the true Pythagorean sum; the discrepancy comes from miscomputing the squares or the root.

2) Angle with the smaller force
- The smaller force is 3333 N, the larger is 5050 N, acting at right angles. The resultant makes an angle theta with the smaller force such that tan(theta) = opposite/adjacent = 5050 / 3333.
- Compute the ratio: 5050 / 3333 ≈ 1.515.
- theta = arctan(1.515) ≈ 56.7 degrees.
- Rounding to the nearest integer gives theta ≈ 57 degrees.

Summary observations:
- The magnitude of the resultant is governed by the Pythagorean sum and is approximately 6051 N, not 6034 N; a value like 6034 would correspond to a slightly smaller resultant and indicates a small arithmetic slip in squaring or summing.
- The angle with the smaller force is about 57 degrees, which aligns with the arctangent of the ratio of the perpendicular forces.

If you want, I can show an alternate rounding path or verify with a quick calculator check to confirm the 6051 N magnitude and 57° angle.

Quiz:MOD 11 QUIZ

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