Find the acceleration of a box being pulled with an applied force of 320.0N at an angle of 30° from the horizontal. The µk between the floor and the box is 0.30
the box weighs 80 kg
Mg = 80*9.8 = 784 N. = Wt. of box = Normal force, Fn.
F = 320*cos30 = 277 N. = hor. component of applied force.
u*Fn = 0.3*784 = 235 N. = Force of kinetic friction.
F-u*Fn = M*a
277-235 = 80a
a = ____ m/s^2.
To find the acceleration of the box being pulled, we can use Newton's second law of motion, which states that the force applied is equal to the product of mass and acceleration (F = m * a).
First, we need to find the horizontal and vertical components of the applied force. The horizontal component of the force can be calculated as F_horizontal = F_applied * cos(theta) while the vertical component can be calculated as F_vertical = F_applied * sin(theta), where theta is the angle of the applied force from the horizontal.
Given:
F_applied = 320.0 N
theta = 30°
m = 80 kg
µ_k = 0.30
Let's calculate the horizontal and vertical components of the force:
F_horizontal = 320.0 N * cos(30°) = 320.0 N * 0.866 = 277.12 N (rounded to two decimal places)
F_vertical = 320.0 N * sin(30°) = 320.0 N * 0.5 = 160.00 N
Now, let's calculate the force of friction that acts in the opposite direction of motion. The force of friction can be determined using the equation F_friction = µ_k * N, where µ_k is the coefficient of kinetic friction and N is the normal force. In this case, we can assume the normal force is equal to the weight of the box, which can be calculated as N = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
N = 80 kg * 9.8 m/s^2 = 784 N
F_friction = 0.30 * 784 N = 235.20 N
Since the force of friction opposes the horizontal force applied, it acts in the opposite direction. Therefore, the net horizontal force can be calculated as:
F_net_horizontal = F_horizontal - F_friction = 277.12 N - 235.20 N = 41.92 N
Using Newton's second law, F = m * a, with the horizontal forces:
F_net_horizontal = m * a
Let's solve for the acceleration:
41.92 N = 80 kg * a
a = 41.92 N / 80 kg
a ≈ 0.524 m/s² (rounded to three decimal places)
Therefore, the acceleration of the box being pulled with an applied force of 320.0 N at an angle of 30° from the horizontal is approximately 0.524 m/s².