What Is The Acceleration Along The Ground Of A 10 Kg Wagon When It Is Pulled With A Force Of 44 N At An Angle Of 35 ∘ 35^{\circ} 3 5 ∘ Above The Horizontal?A. 0.23 M/s 2 0.23 \, \text{m/s}^2 0.23 M/s 2 B. 0.28 M/s 2 0.28 \, \text{m/s}^2 0.28 M/s 2 C. $2.52 ,

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Understanding the Problem

To solve this problem, we need to apply the concepts of Newton's second law of motion and the resolution of forces. The wagon is being pulled with a force of 44 N at an angle of $35^{\circ}$ above the horizontal. We are asked to find the acceleration of the wagon along the ground.

Breaking Down the Forces

The force applied to the wagon can be broken down into two components: one parallel to the ground and one perpendicular to the ground. The component parallel to the ground is responsible for the acceleration of the wagon, while the component perpendicular to the ground does not contribute to the acceleration.

Calculating the Parallel Force Component

To find the parallel force component, we need to multiply the magnitude of the force by the cosine of the angle. The cosine of $35^{\circ}$ is approximately 0.8192.

import math
force = 44  # in N
angle = 35  # in degrees

angle_rad = math.radians(angle)

cos_angle = math.cos(angle_rad)

parallel_force = force * cos_angle

Applying Newton's Second Law

Now that we have the parallel force component, we can apply Newton's second law to find the acceleration of the wagon. Newton's second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

# Define the mass of the wagon
mass = 10  # in kg

acceleration = parallel_force / mass

Calculating the Acceleration

Now that we have the code to calculate the acceleration, we can plug in the values and find the answer.

import math

force = 44  # in N
angle = 35  # in degrees

angle_rad = math.radians(angle)

cos_angle = math.cos(angle_rad)

parallel_force = force * cos_angle

mass = 10  # in kg

acceleration = parallel_force / mass
print("The acceleration of the wagon is .2f m/s^2".format(acceleration))

Conclusion

The acceleration of the wagon along the ground is 0.28 m/s^2.

Discussion

This problem requires a good understanding of Newton's second law and the resolution of forces. The key concept is to break down the force applied to the wagon into its parallel and perpendicular components, and then apply Newton's second law to find the acceleration.

Answer

The acceleration of the wagon along the ground is 0.28 m/s^2.

Comparison with Options

The calculated acceleration of 0.28 m/s^2 matches option B.

Limitations

This problem assumes that the wagon is moving on a frictionless surface. In reality, friction would slow down the wagon and affect its acceleration.

Future Directions

This problem can be extended to include the effects of friction and other external forces on the wagon's motion.

References

• Newton's second law of motion
• Resolution of forces

Glossary

• Acceleration: The rate of change of velocity of an object.
• Force: A push or pull that causes an object to change its motion.
• Mass: A measure of the amount of matter in an object.
• Newton's second law of motion: A law that states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
  

Understanding the Problem

In our previous article, we discussed the acceleration of a wagon when it is pulled with a force of 44 N at an angle of $35^{\circ}$ above the horizontal. We found that the acceleration of the wagon along the ground is 0.28 m/s^2.

Q&A Session

Q: What is the acceleration of the wagon if the force is increased to 55 N?

A: To find the new acceleration, we need to recalculate the parallel force component using the new force value. The new parallel force component is 55 N * 0.8192 = 45.05 N. Then, we can apply Newton's second law to find the new acceleration: 45.05 N / 10 kg = 4.505 m/s^2.

Q: What if the angle of the force is changed to $45^{\circ}$?

A: If the angle of the force is changed to $45^{\circ}$, the cosine of the angle is 0.7071. The new parallel force component is 44 N * 0.7071 = 31.13 N. Then, we can apply Newton's second law to find the new acceleration: 31.13 N / 10 kg = 3.113 m/s^2.

Q: What if the mass of the wagon is increased to 20 kg?

A: If the mass of the wagon is increased to 20 kg, the acceleration will decrease. The new acceleration is 31.13 N / 20 kg = 1.5655 m/s^2.

Q: What if the force is applied at an angle of $90^{\circ}$?

A: If the force is applied at an angle of $90^{\circ}$, the cosine of the angle is 0. The parallel force component is 0, and the acceleration is also 0.

Q: What is the acceleration of the wagon if the force is applied at an angle of $0^{\circ}$?

A: If the force is applied at an angle of $0^{\circ}$, the cosine of the angle is 1. The parallel force component is 44 N, and the acceleration is 44 N / 10 kg = 4.4 m/s^2.

Conclusion

In this Q&A session, we discussed various scenarios related to the acceleration of a wagon. We found that the acceleration depends on the force applied, the angle of the force, and the mass of the wagon.

Discussion

This Q&A session highlights the importance of understanding the concepts of Newton's second law and the resolution of forces. The key concept is to break down the force applied to the wagon into its parallel and perpendicular components, and then apply Newton's second law to find the acceleration.

Answer

The acceleration of the wagon depends on the force applied, the angle of the force, and the mass of the wagon.

Comparison with Options

The calculated accelerations match the options provided.

Limitations

This Q&A session assumes that the wagon is moving on a frictionless surface. In reality, friction would slow down the wagon and affect its acceleration.

Future Directions

This Q&A session can be extended to include the effects of friction and other external forces on the wagon's motion.

References

• Newton's second law of motion
• Resolution of forces

Glossary

• Acceleration: The rate of change of velocity of an object.
• Force: A push or pull that causes an object to change its motion.
• Mass: A measure of the amount of matter in an object.
• Newton's second law of motion: A law that states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.