A man applies a force of 150 N to pull a 20kg box with a rope that makes an angle of 60 degrees with the horizontal. The box experiences a kinetic friction of 15 N. calculate the acceleration.
net force=ma
net force also equals 150*cos60-weightcomponet-15
where the weight component along the plane=mg*sin60
the result of all this is
150*cos60-mg*sin60-15=ma
solve for acceleation a.
To calculate the acceleration of the box, we need to consider the forces acting on it.
1. Resolve the applied force into horizontal and vertical components:
-- The horizontal component of the applied force can be calculated as F_horizontal = F_applied * cos(theta), where F_applied is the applied force (150 N) and theta is the angle (60 degrees).
-- The vertical component of the applied force (F_vertical) can be calculated as F_vertical = F_applied * sin(theta).
2. Determine the net force acting on the box in the horizontal direction:
-- The net force acting on the box in the horizontal direction is the difference between the horizontal component of the applied force (F_horizontal) and kinetic friction (f_kinetic): Net force (F_net) = F_horizontal - f_kinetic.
3. Calculate the acceleration using Newton's second law:
-- The acceleration (a) can be calculated using the formula F_net = m * a, where F_net is the net force and m is the mass of the box.
Let's calculate step-by-step:
1. Calculating the horizontal and vertical components of the applied force:
F_horizontal = 150 N * cos(60 degrees) = 150 N * 0.5 = 75 N
F_vertical = 150 N * sin(60 degrees) = 150 N * 0.866 = 129.9 N
2. Determining the net force acting on the box in the horizontal direction:
F_net = F_horizontal - f_kinetic
= 75 N - 15 N
= 60 N
3. Calculating the acceleration:
F_net = m * a
60 N = 20 kg * a
Divide both sides of the equation by 20 kg:
a = 60 N / 20 kg = 3 m/s²
Therefore, the acceleration of the box is 3 m/s².
To calculate the acceleration of the box, we need to consider the net force acting on the box. The net force is the vector sum of all the forces acting on the box.
Let's break down the forces acting on the box:
1. The force applied by the man: The magnitude of this force is 150 N. Since the rope makes an angle of 60 degrees with the horizontal, we need to find the horizontal component of this force. The horizontal component is given by Fcosθ, where F is the force and θ is the angle. Therefore, the horizontal component of the applied force is 150 N * cos(60°).
2. The force of kinetic friction: The magnitude of this force is 15 N, and it acts in the opposite direction of motion. Since we are calculating acceleration, which is the rate of change of velocity, the direction of this force doesn't matter. We will consider it as a negative force.
Now, let's calculate the net force:
Net force = Force applied - Force of friction
= [150 N * cos(60°)] - 15 N
Finally, we can use Newton's second law of motion to calculate the acceleration:
Net force = mass * acceleration
Rearranging the equation, we get:
acceleration = Net force / mass
Substituting the values, we have:
acceleration = ([150 N * cos(60°)] - 15 N) / 20 kg
Now, let's calculate the acceleration:
acceleration = (150 N * cos(60°) - 15 N) / 20 kg
Using the value of cos(60°) ≈ 0.5, we can simplify the equation further:
acceleration = (150 N * 0.5 - 15 N) / 20 kg
acceleration = (75 N - 15 N) / 20 kg
acceleration = 60 N / 20 kg
acceleration = 3 m/s²
Therefore, the acceleration of the box is 3 m/s².