### Physics Problem: Determining Acceleration from Forces#### Problem Statement:Only two forces act on an object (mass = 4.19 kg), as depicted in the drawing. Find (a) the magnitude and (b) the direction (relative to the x-axis) of the acceleration of the object.#### Diagram Description:The diagram shows the object, representing as a block, on which two forces are acting. The forces are depicted as arrows:- A 40.0 N force acting horizontally to the right (along the +x axis).- A 60.0 N force acting at a 45.0° angle above the horizontal.#### Questions:(a) Calculate the magnitude of the acceleration of the object.(b) Determine the direction of the acceleration relative to the x-axis.#### Response Fields:- (a) Number: ______ [Units: m/s²]- (b) Number: ______ [Units: Degrees]Ensure to fill in the values accurately in the provided fields.#### Explanation:To solve for the magnitude and direction of the acceleration, follow these detailed steps:1. **Resolve the 60.0 N force into its components:** - Horizontal component: $60.0 \, \text{N} \cos(45.0°)$ - Vertical component: $60.0 \, \text{N} \sin(45.0°)$2. **Sum up the forces in the x and y directions:** - $F_x = 40.0 \, \text{N} + 60.0 \, \text{N} \cos(45.0°)$ - $F_y = 60.0 \, \text{N} \sin(45.0°)$3. **Calculate the net force $F_{net}$:** - $F_{net} = \sqrt{(F_x)^2 + (F_y)^2}$4. **Determine the acceleration using Newton's second law:** - $a = \frac{F_{net}}{m}$5. **Find the direction of the acceleration:** - The angle θ with respect to the x-axis can be determined using $\tan^{-1} \left(\frac{F_y}{F_x} \right)$This systematic approach ensures you obtain both the magnitude and the direction of the acceleration accurately.

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Description: ### Physics Problem: Determining Acceleration from Forces#### Problem Statement:Only two forces act on an object (mass = 4.19 kg), as depicted in the drawing. Find (a) the magnitude and (b) the direction (relative to the x-axis) of the acceleration

The resultant of the two forces is given by parallelogram law, F=402+602+2×40×60×cos(45o)=92.7 N The…

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Only two forces act on an object (mass=4.19 kg), as the drawing. Find (a) the magnitude and (b) the direction (relative to the x axis) of the acceleration of the object. +V I I 145.0⁰ 40.0 N 60.0 N ---+x

Only two forces act on an object (mass=4.19 kg), as the drawing. Find (a) the magnitude and (b) the direction (relative to the x axis) of the acceleration of the object. +V I I 145.0⁰ 40.0 N 60.0 N ---+x

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### Physics Problem: Determining Acceleration from Forces

#### Problem Statement:
Only two forces act on an object (mass = 4.19 kg), as depicted in the drawing. Find (a) the magnitude and (b) the direction (relative to the x-axis) of the acceleration of the object.

#### Diagram Description:
The diagram shows the object, representing as a block, on which two forces are acting. The forces are depicted as arrows:
- A 40.0 N force acting horizontally to the right (along the +x axis).
- A 60.0 N force acting at a 45.0° angle above the horizontal.

#### Questions:
(a) Calculate the magnitude of the acceleration of the object.
(b) Determine the direction of the acceleration relative to the x-axis.

#### Response Fields:
- (a) Number: ______ [Units: m/s²]
- (b) Number: ______ [Units: Degrees]

Ensure to fill in the values accurately in the provided fields.

#### Explanation:
To solve for the magnitude and direction of the acceleration, follow these detailed steps:

1. **Resolve the 60.0 N force into its components:**
- Horizontal component: $60.0 \, \text{N} \cos(45.0°)$
- Vertical component: $60.0 \, \text{N} \sin(45.0°)$

2. **Sum up the forces in the x and y directions:**
- $F_x = 40.0 \, \text{N} + 60.0 \, \text{N} \cos(45.0°)$
- $F_y = 60.0 \, \text{N} \sin(45.0°)$

3. **Calculate the net force $F_{net}$:**
- $F_{net} = \sqrt{(F_x)^2 + (F_y)^2}$

4. **Determine the acceleration using Newton's second law:**
- $a = \frac{F_{net}}{m}$

5. **Find the direction of the acceleration:**
- The angle θ with respect to the x-axis can be determined using $\tan^{-1} \left(\frac{F_y}{F_x} \right)$

This systematic approach ensures you obtain both the magnitude and the direction of the acceleration accurately.

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