two forces act on a moving object with a mass of 27kg.one force has a magnitude of 12N and points south, while the other has a magnitude of 17N and points due west. Whats the acceleration of the object?
The magnitude of the net force is
F =sqrt[(12N)^2+ (17N)^2]
= 20.80N
The acceleration of the object is
a = F/m
Here m = 27 kg
Substitute the values for a.
4
To find the acceleration of the object, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Mass of the object (m) = 27 kg
Force 1 (F1) = 12 N (south)
Force 2 (F2) = 17 N (west)
First, we need to break down the forces into their horizontal and vertical components:
Force 1 (F1):
- Vertical component (F1y) = 0 N (no vertical component)
- Horizontal component (F1x) = 12 N (south)
Force 2 (F2):
- Vertical component (F2y) = 0 N (no vertical component)
- Horizontal component (F2x) = 17 N (west)
Now, let's find the net horizontal and vertical forces:
Net horizontal force (Fnet_x) = F1x + F2x
= 12 N (south) + 17 N (west)
= -12 N (south) + 17 N (east)
= 17 N (east) - 12 N (south)
= 5 N (east)
Net vertical force (Fnet_y) = F1y + F2y
= 0 N (no vertical component) + 0 N (no vertical component)
= 0 N
We can now find the net force vector (Fnet) using the horizontal and vertical components:
Fnet = √(Fnet_x^2 + Fnet_y^2)
= √(5^2 + 0^2)
= √25
= 5 N
Finally, we can calculate the acceleration (a) using Newton's second law:
Fnet = m * a
5 N = 27 kg * a
a = 5 N / 27 kg
a ≈ 0.185 m/s²
Therefore, the acceleration of the object is approximately 0.185 m/s².
To find the acceleration of the object, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be written as:
acceleration = net force / mass
In this case, we have two forces acting on the object:
1. A force of magnitude 12 N pointing south.
2. A force of magnitude 17 N pointing due west.
To find the net force, we need to combine these two forces. Since the forces are acting in different directions (south and west), we need to use vector addition to find the net force.
Step 1: Draw a diagram representing the forces:
- Represent the force pointing south as a downward arrow with a length of 12 units.
- Represent the force pointing due west as a leftward arrow with a length of 17 units.
Step 2: Use vector addition to find the resultant force:
- Draw a third arrow connecting the tails of the two arrows.
- Measure the length of this arrow, which represents the magnitude of the resultant force.
Step 3: Use trigonometry to determine the magnitude and direction of the resultant force:
- Apply the Pythagorean theorem to determine the magnitude of the resultant force.
- Use inverse trigonometric functions to determine the direction of the resultant force.
Once you have determined the magnitude and direction of the resultant force, you can use Newton's second law to find the acceleration by dividing the net force by the mass of the object:
acceleration = resultant force / mass
Plug in the values you have obtained for the resultant force and the mass of the object (27 kg) to calculate the acceleration.