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

View Explanation

Log in for full answers

Similar Questions

Vector A in the drawing is equal to

Vector A in the drawing is equal to

The figure below shows two forces F1 and F2 acting together on an object. Which of the red vectors represents the resultant force F1+F2, in terms of the direction and magnitude?

A student walks 1.0 km east and then 3.0 km south. The student then walks 5.0 km west. The magnitude of the student's displacement is

A student walks 14.4 km east and then 8.3 km north. After that, the student walks 2.3 km east. The magnitude of the student's displacement is

A person walks 454 m East, followed by 337.9 m South and finally 1446.9 m West. What is this person's displacement vector taking reference from the starting position?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler