A wagon is used to help deliver papers. There is a force applied at an angle of 25 degrees to the horizontal that causes the wagon to move a distance of 15m[N] in 10.0s from rest. There is a force of friction of 3.1 N acting on the 27kg wagon.
What is the acceleration of the wagon?
s=at^2/2
a =2•s/t^2 =2•15/100 = 0.3 m/s^2
To find the acceleration of the wagon, 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 is the difference between the applied force and the force of friction. In this case, the applied force is at an angle of 25 degrees to the horizontal. We need to find the horizontal component of this force.
To calculate the horizontal component, we can use the formula:
Horizontal component = Applied force * cos(angle)
Given:
Applied force = 15 N
Angle = 25 degrees
Using this information, we can calculate the horizontal component of the applied force:
Horizontal component = 15 N * cos(25 degrees)
Now, we can calculate the net force:
Net force = Horizontal component - force of friction
Given:
Force of friction = 3.1 N
We can now substitute the values into the formula and find the net force:
Net force = (15 N * cos(25 degrees)) - 3.1 N
Next, we can calculate the acceleration using Newton's second law:
Net force = mass * acceleration
Given:
Mass = 27 kg
Rearranging the equation, we can solve for acceleration:
Acceleration = Net force / mass
Substituting the values we found earlier, we get:
Acceleration = [(15 N * cos(25 degrees)) - 3.1 N] / 27 kg
Calculating this expression gives us the acceleration of the wagon.