A 75kg box is being pulled across the floor with a force of 465N.If the kinetic coefficient of friction is 0.57,what is the acceleration of the box?
To find the acceleration of the box, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's calculate the force of friction acting on the box:
Force of Friction = Kinetic Coefficient of Friction * Normal Force
The normal force is the force exerted by a surface perpendicular to the object. In this case, the box is on a flat horizontal surface, so the normal force is equal to the weight of the box.
Normal Force = Mass * Gravity
The mass of the box is given as 75 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Normal Force = 75 kg * 9.8 m/s^2
Next, we can calculate the force of friction using the given kinetic coefficient of friction:
Force of Friction = 0.57 * Normal Force
Now, we need to determine the net force acting on the box. In this case, the only force acting on the box is the applied force of 465 N.
Net Force = Applied Force - Force of Friction
Finally, we can use Newton's second law of motion to calculate the acceleration of the box:
Acceleration = Net Force / Mass
Substituting the values we calculated earlier:
Acceleration = (Applied Force - Force of Friction) / Mass
Acceleration = (465 N - (0.57 * (75 kg * 9.8 m/s^2))) / 75 kg
Simplifying the equation will give us the value of acceleration.