A student pulls a box of books on a smooth horizontal floor, ignore friction with a force of 131 N in a direction of 37° above the horizontal. If the mass of the box and the books is 33.7 kg, what is the acceleration of the box?
horizontal F = 131 cos 37 = m a = 33.7 a
so
a = (131/33.7)cos 37
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.
The given force applied to the box is 131 N at an angle of 37° above the horizontal. We need to break down this force into its horizontal and vertical components.
The horizontal component of the force can be calculated using the formula: F_horizontal = F * cos(theta), where F is the magnitude of the force (131 N) and theta is the angle of the force (37°).
F_horizontal = 131 N * cos(37°) = 105.61 N
The vertical component of the force can be calculated using the formula: F_vertical = F * sin(theta), where F is the magnitude of the force (131 N) and theta is the angle of the force (37°).
F_vertical = 131 N * sin(37°) = 78.99 N
Since there is no vertical acceleration (the box is on a smooth horizontal floor), this vertical component of the force does not affect the box's acceleration. Therefore, we can ignore it when calculating the acceleration.
Now, we have the horizontal force (105.61 N) and the mass of the box and books (33.7 kg). We can apply Newton's second law of motion to find the acceleration.
Acceleration = Force / Mass
Acceleration = 105.61 N / 33.7 kg = 3.13 m/s^2
So, the acceleration of the box is 3.13 m/s^2.
To find the acceleration of the box, we first need to resolve the applied force into its horizontal and vertical components.
1. Resolve the force:
The horizontal component (F_x) is calculated by multiplying the force (F) by the cosine of the angle (37°):
F_x = F * cos(37°)
= 131 N * cos(37°)
≈ 105.13 N
The vertical component (F_y) is calculated by multiplying the force (F) by the sine of the angle (37°):
F_y = F * sin(37°)
= 131 N * sin(37°)
≈ 79.15 N
2. Calculate the net force in the horizontal direction (F_net_x):
Since there is no friction mentioned, the only force acting on the box in the x-direction is the horizontal component of the applied force.
F_net_x = F_x = 105.13 N
3. Use Newton's second law of motion to find the acceleration (a):
Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object.
F_net_x = m * a
Rearranging the formula, we get:
a = F_net_x / m
= 105.13 N / 33.7 kg
≈ 3.12 m/s²
Therefore, the acceleration of the box is approximately 3.12 m/s².