Only two forces act on an object (mass = 4.96 kg), as in the drawing. Find the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the object. (a) Number i (b) Number i Units Units +y 60.0 N 40.0 N
Only two forces act on an object (mass = 4.96 kg), as in the drawing. Find the (a) magnitude and (b) direction (relative to the x axis) of the acceleration of the object. (a) Number i (b) Number i Units Units +y 60.0 N 40.0 N
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![## Problem Statement
Only two forces act on an object (mass = 4.96 kg), as shown in the drawing. Find the (a) magnitude and (b) direction (relative to the x-axis) of the acceleration of the object.
## Diagram Explanation
In the diagram, a wooden block is subjected to two forces:
- A downward force of 60.0 N acts along the negative y-axis.
- A horizontal force of 40.0 N acts along the positive x-axis.
Both forces are represented with arrows originating from the center of the block, indicating the direction and magnitude of each force.
### Questions
(a) Find the magnitude of the acceleration.
- Input Field: Number
- Units Dropdown: Select units from the dropdown menu (e.g., m/s²).
(b) Find the direction of the acceleration relative to the x-axis.
- Input Field: Number
- Units Dropdown: Select units from the dropdown menu (e.g., degrees).
### How to Solve
1. **Calculate the resultant force:**
Since the forces are perpendicular to each other, we can use the Pythagorean theorem to find the resultant force (F):
\[
F = \sqrt{(F_x)^2 + (F_y)^2}
\]
where \( F_x = 40.0 \text{ N} \) and \( F_y = -60.0 \text{ N} \).
2. **Calculate the magnitude of the acceleration (a):**
Use Newton's second law \( F = ma \):
\[
a = \frac{F}{m}
\]
where \( m = 4.96 \text{ kg} \).
3. **Calculate the direction of the acceleration (θ) relative to the x-axis:**
The direction θ can be found using trigonometry:
\[
\theta = \tan^{-1} \left( \frac{F_y}{F_x} \right)
\]
### Input Fields
- (a) Magnitude of the acceleration
- Numerical input for the calculated magnitude.
- Select appropriate units from the dropdown.
- (b) Direction of the acceleration
- Numerical input for the calculated direction.
- Select degrees or other appropriate units from the dropdown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0a09bd-ef71-43b6-abcd-653755da1dfb%2Fab1f69cb-1405-4a94-9ccf-482d0fb43b32%2Fd766xqr_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement
Only two forces act on an object (mass = 4.96 kg), as shown in the drawing. Find the (a) magnitude and (b) direction (relative to the x-axis) of the acceleration of the object.
## Diagram Explanation
In the diagram, a wooden block is subjected to two forces:
- A downward force of 60.0 N acts along the negative y-axis.
- A horizontal force of 40.0 N acts along the positive x-axis.
Both forces are represented with arrows originating from the center of the block, indicating the direction and magnitude of each force.
### Questions
(a) Find the magnitude of the acceleration.
- Input Field: Number
- Units Dropdown: Select units from the dropdown menu (e.g., m/s²).
(b) Find the direction of the acceleration relative to the x-axis.
- Input Field: Number
- Units Dropdown: Select units from the dropdown menu (e.g., degrees).
### How to Solve
1. **Calculate the resultant force:**
Since the forces are perpendicular to each other, we can use the Pythagorean theorem to find the resultant force (F):
\[
F = \sqrt{(F_x)^2 + (F_y)^2}
\]
where \( F_x = 40.0 \text{ N} \) and \( F_y = -60.0 \text{ N} \).
2. **Calculate the magnitude of the acceleration (a):**
Use Newton's second law \( F = ma \):
\[
a = \frac{F}{m}
\]
where \( m = 4.96 \text{ kg} \).
3. **Calculate the direction of the acceleration (θ) relative to the x-axis:**
The direction θ can be found using trigonometry:
\[
\theta = \tan^{-1} \left( \frac{F_y}{F_x} \right)
\]
### Input Fields
- (a) Magnitude of the acceleration
- Numerical input for the calculated magnitude.
- Select appropriate units from the dropdown.
- (b) Direction of the acceleration
- Numerical input for the calculated direction.
- Select degrees or other appropriate units from the dropdown.
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