A 15.5 kg block is pulled by two forces. The first is 11.8 N at a 53.7° angle and the second is 22.9 N at a
-15.8° angle. What is the magnitude of the acceleration? magnitude (m/s^2)
To find the magnitude of acceleration, we can first find the net force acting on the block.
First, let's break down the given forces into their x and y components.
The first force of 11.8 N at a 53.7° angle can be broken down into:
Force1x = 11.8 N * cos(53.7°)
Force1y = 11.8 N * sin(53.7°)
The second force of 22.9 N at a -15.8° angle can be broken down into:
Force2x = 22.9 N * cos(-15.8°)
Force2y = 22.9 N * sin(-15.8°)
Note that sine of -15.8° is the same as the sine of 15.8° since sine is an odd function.
Now, let's find the net force in the x-direction by summing up the x-components of the forces:
Net force in x-direction (ΣFx) = Force1x + Force2x
Substituting the values:
ΣFx = 11.8 N * cos(53.7°) + 22.9 N * cos(-15.8°)
Now, let's find the net force in the y-direction by summing up the y-components of the forces:
Net force in y-direction (ΣFy) = Force1y + Force2y
Substituting the values:
ΣFy = 11.8 N * sin(53.7°) + 22.9 N * sin(-15.8°)
Now we can calculate the net force by using the Pythagorean theorem:
Net force (ΣF) = √(ΣFx)^2 + (ΣFy)^2
Substituting the values calculated before:
ΣF = √[(11.8 N * cos(53.7°) + 22.9 N * cos(-15.8°))^2 + (11.8 N * sin(53.7°) + 22.9 N * sin(-15.8°))^2]
Next, we can use Newton's second law to find the magnitude of the acceleration:
ΣF = mass * acceleration
Substituting the given mass (15.5 kg):
√[(11.8 N * cos(53.7°) + 22.9 N * cos(-15.8°))^2 + (11.8 N * sin(53.7°) + 22.9 N * sin(-15.8°))^2] = 15.5 kg * acceleration
Now, we can solve for the acceleration:
acceleration = √[(11.8 N * cos(53.7°) + 22.9 N * cos(-15.8°))^2 + (11.8 N * sin(53.7°) + 22.9 N * sin(-15.8°))^2] / 15.5 kg
Calculating this equation will give you the magnitude of the acceleration in m/s^2.