Proper Calculation of Acceleration in Two-Force Problems

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In summary, the problem involves a 3.0 kg body with two horizontal forces acting on it, one of 9.0N due east and the other of 8.0N at 62° north of west. The magnitude of the body's acceleration is found to be 2.9m/s^2 by taking into account both the x and y directions. In a similar question in the book, where a puck with a weight of 0.20 kg has F1 of magnitude 1N pointing 30 degrees below the horizontal and F2 of magnitude 2N pointing west, the book only takes into account the x direction and finds the acceleration to be -5.7 m/s^2. It is
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Homework Statement



Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0N, acting due east, and the other is 8.0N acting 62° north of west. What is the magnitude of the body's acceleration.

Okay I know the answer is 2.9m/s^2.

It is from F1 = 9i + oj

F2 = -8cos62 + 8sin62

Fnet = 5.2i + 7.1j

Resultant vector = sqrt [(5.2^2) + (7.1^2)]

=8.8
F = ma

8.8/3 = a

a = 2.9.


Now in the book, they had a similar question asking: to find the acceleration of a puck when there was F1 of magnitude 1N pointing 30 degrees below the horizontal and F2 of magnitude 2N pointing west of the puck. The puck weighs .20 kg.

They only used (1Ncos30 - 2N)/0.20 = a

a = -5.7 m/s^2

Now I am asking which way is correct? because in the first example i got the correct answer with both x and y directions taken in account for. but in the book's example they only found the x direction.

Homework Equations



F = ma

The Attempt at a Solution

 
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  • #2
F1 of magnitude 1N pointing 30 degrees below the horizontal
This might mean pointing into the ground at 30 degrees, and with F2 exactly opposing the horizontal component of this, making the relevant components of F1 and F2 to be co-linear.
 
  • #3
So i don't take into account the y direction when it's pointing into the ground, but I do if it's pointing out of the ground?
 

FAQ: Proper Calculation of Acceleration in Two-Force Problems

1. What is the proper way to find forces?

The proper way to find forces is by using Newton's Laws of Motion. These laws state that an object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by an external force. To find forces, you must first identify all the objects involved in the situation and then apply the laws of motion to determine the forces acting on each object.

2. How do I calculate the magnitude and direction of a force?

To calculate the magnitude and direction of a force, you must use vector addition. This involves breaking the force down into its horizontal and vertical components and then using trigonometry to find the magnitude and direction of each component. Once you have the magnitude and direction of each component, you can use the Pythagorean theorem to find the overall magnitude of the force and use inverse trigonometric functions to find the direction.

3. What are the different types of forces?

There are several types of forces, including gravitational, electromagnetic, frictional, and normal forces. Gravitational forces are caused by the mass of an object and pull objects towards each other. Electromagnetic forces are caused by the interaction of electrically charged particles. Frictional forces act in the opposite direction of an object's motion and can cause objects to slow down or stop. Normal forces are perpendicular to a surface and prevent objects from passing through it.

4. What is the difference between a balanced and unbalanced force?

A balanced force is one where the net force on an object is equal to zero, meaning that the forces acting on the object are canceling each other out. This results in no change in the object's motion. An unbalanced force, on the other hand, has a net force that is not equal to zero, causing the object to accelerate in the direction of the net force.

5. How can I apply the concept of forces in real-life situations?

Forces are present in almost every aspect of our daily lives. They can be applied in situations such as pushing a shopping cart, throwing a ball, or driving a car. Understanding the concept of forces can also help engineers in designing structures that can withstand external forces, and it can aid scientists in studying the motion of celestial bodies in space. Additionally, understanding forces can help individuals make informed decisions, such as wearing a seatbelt to counteract the unbalanced force of a car accident.

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