a student pushes a 10 kg box across a warehouse floor. if the boz accelerates at 3 m/s/s and the force of friction is 20 newtons. determine the size of the students applied force?
Fn = Fap - Ff = ma,
Fap - 20 = 10 * 3 = 30N,
Fap = 30 + 20 = 50N = Applied force.
To determine the size of the student's applied force, we will 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.
Given:
Mass of the box (m) = 10 kg
Acceleration (a) = 3 m/s²
Force of friction (F_friction) = 20 N
Step 1: Calculate the force due to friction:
The force of friction opposes the motion and can be determined using the equation:
F_friction = μ * N
Where μ is the coefficient of friction and N is the normal force.
However, in this case, the coefficient of friction and the normal force are not given, but we know that the box is accelerating. When an object is accelerating, the net force acting on it is the difference between the applied force and the force of friction:
Net force = applied force - force of friction
Step 2: Calculate the net force:
Net force = mass * acceleration
Given that the acceleration (a) is 3 m/s² and the mass (m) is 10 kg, we can substitute these values into the equation to calculate the net force.
Net force = 10 kg * 3 m/s²
Net force = 30 N
Step 3: Determine the applied force:
Now, we can use the net force and force of friction values to calculate the applied force.
Net force = applied force - force of friction
Substituting the given values into the equation:
30 N = applied force - 20 N
Step 4: Solve for the applied force:
To isolate the applied force, we rearrange the equation:
applied force = net force + force of friction
applied force = 30 N + 20 N
applied force = 50 N
Therefore, the size of the student's applied force is 50 Newtons.