A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 30° above the horizontal. If the mass of the box and the books is 40.0 kg, what is the acceleration of the box?
Square root of three meters per second squared.
Four square root of three over five; meters per second squared.
five square roots of three all over four meters per second squared
Square of five meters per second squared.
Five square roots of two all over two meters per second squared
F = 100 cos 30 = 86.6 N = 100 (sqrt 3)/2
a = F/m = 86.6/40 = 2.17 m/s^2 =(100/80)sqrt 3 = (5/4) sqrt 3 m/s^2
so
five square roots of three all over four meters per second squared
Well, this problem is really trying to calculate the acceleration of the box. But I think it's also trying to confuse you with all those square roots and fractions. So, let's break it down.
First, we need to resolve the force into its horizontal and vertical components. The force is acting at an angle of 30° above the horizontal, so the horizontal component will be the force multiplied by the cosine of 30°. That gives us:
Horizontal component = 100 N * cos(30°)
Now, the vertical component will be the force multiplied by the sine of 30°. That gives us:
Vertical component = 100 N * sin(30°)
Since we're dealing with a smooth surface, the vertical component doesn't really matter in terms of the box's acceleration. So, let's focus on the horizontal component.
The acceleration of the box can be calculated using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the horizontal component of the force, and the mass is given as 40 kg.
Net force = Horizontal component = 100 N * cos(30°)
Mass = 40 kg
Acceleration = Unknown
So, we can rearrange the equation to solve for acceleration:
Acceleration = Net force / Mass
Acceleration = (100 N * cos(30°)) / 40 kg
Now, let's simplify that expression:
Acceleration = (100 N * √3/2) / 40 kg
Acceleration = (100 N * √3) / (2 * 40 kg)
Acceleration = (100 N * √3) / 80 kg
We can further simplify the expression:
Acceleration = (5/4) * √3 meters per second squared
So, the correct answer is "Four square root of three over five; meters per second squared." Funny how math sometimes makes us go in circles, isn't it?
To find the acceleration of the box, we need to resolve the applied force into its horizontal and vertical components.
The horizontal component of the force can be found using trigonometry:
Horizontal component = applied force * cos(angle)
Horizontal component = 100 N * cos(30°)
Horizontal component ≈ 100 N * (0.866)
Horizontal component ≈ 86.6 N
The vertical component of the force can also be found using trigonometry:
Vertical component = applied force * sin(angle)
Vertical component = 100 N * sin(30°)
Vertical component ≈ 100 N * (0.5)
Vertical component = 50 N
Since the box is on a horizontal floor, there is no vertical acceleration. The weight of the box cancels out the vertical force. Therefore, the vertical component of the applied force is balanced.
The net force acting on the box is equal to the horizontal component of the applied force:
Net force = horizontal component of the applied force
Net force = 86.6 N
Now, using Newton's second law of motion, we can find the acceleration of the box:
Net force = mass * acceleration
86.6 N = 40.0 kg * acceleration
acceleration = 86.6 N / 40.0 kg
acceleration ≈ 2.165 m/s²
Therefore, the acceleration of the box is approximately 2.165 m/s².
To find the acceleration of the box, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force applied to the box is 100 N at an angle of 30° above the horizontal. We can break down this force into its horizontal and vertical components.
The horizontal component of the force is given by Fx = F * cos(theta), where F is the magnitude of the force (100 N) and theta is the angle (30°).
Fx = 100 N * cos(30°) = 100 N * sqrt(3)/2 ≈ 86.6 N.
Since there are no other horizontal forces acting on the box, the horizontal component of the force is also equal to the mass of the box (40.0 kg) multiplied by its acceleration, Ax.
Ax = Fx / m = 86.6 N / 40.0 kg ≈ 2.17 m/s^2.
Therefore, the acceleration of the box in the horizontal direction is approximately 2.17 m/s^2.
The correct answer is: five square roots of two all over two meters per second squared