A wooden box weighing 271 N is pushed across the floor by a workman who exerts a horizontal force of 144 N. If the force of friction between the box and the floor is 28 N, what is the acceleration (in meters/second^2) of the box?
a = Fnet/M = (144-28)/M = 116/M
The mass is M = 271/g = 27.65 kg
a = 116/27.65 = 4.19 m/s^2
To find the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the net force acting on the box. The net force is the difference between the applied force and the force of friction.
Net force = Applied force - Force of friction
Net force = 144 N - 28 N
Net force = 116 N
Now, we need to find the mass of the box. We can use the formula weight = mass * acceleration due to gravity to find the mass.
Weight = 271 N
Acceleration due to gravity = 9.8 m/s^2 (approximate value)
Weight = mass * 9.8
mass = Weight / 9.8
mass = 271 N / 9.8 m/s^2
mass ≈ 27.76 kg
Now, we can plug in the values into Newton's second law of motion to find the acceleration.
Net force = mass * acceleration
116 N = 27.76 kg * acceleration
acceleration = 116 N / 27.76 kg
acceleration ≈ 4.18 m/s^2
Therefore, the acceleration of the box is approximately 4.18 m/s^2.
To find the acceleration of the box, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The net force acting on the box is the difference between the applied force and the force of friction:
net force = applied force - force of friction
Given that the applied force is 144 N and the force of friction is 28 N, we can calculate the net force:
net force = 144 N - 28 N
net force = 116 N
Now, we need to find the mass of the box. We can use the equation:
weight = mass * acceleration due to gravity
Given that the weight of the box is 271 N and the acceleration due to gravity is approximately 9.8 m/s^2, we can rearrange the equation to solve for the mass:
mass = weight / acceleration due to gravity
mass = 271 N / 9.8 m/s^2
mass ≈ 27.7 kg
Finally, we can substitute the values of the net force and the mass into Newton's second law to find the acceleration:
net force = mass * acceleration
116 N = 27.7 kg * acceleration
Solving for acceleration:
acceleration = net force / mass
acceleration = 116 N / 27.7 kg
acceleration ≈ 4.19 m/s^2
Therefore, the acceleration of the box is approximately 4.19 m/s^2.