a 70 kg box slides along the floor by a 400N force. the coefficient of friction between the box and the floor is 0.50 when the box is sliding. find the acceleration of the box.
Use Fnet = M*a and solve for a
Fnet = Fapplied - Ffriction
Ffriction = M*g*mu_k = 343 N
Put it all together
To find the acceleration of the box, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, the force acting on the box is the force of friction, which can be calculated using the formula:
Force of friction = coefficient of friction * normal force
The normal force is the force exerted by a surface to support the weight of an object resting on it. Since the box is sliding, the normal force is equal to the force of gravity acting on the box, which is the product of the mass of the box (70 kg) and the acceleration due to gravity (9.8 m/s^2):
Normal force = mass * acceleration due to gravity
Normal force = 70 kg * 9.8 m/s^2
Normal force = 686 N
Now, we can calculate the force of friction:
Force of friction = coefficient of friction * normal force
Force of friction = 0.50 * 686 N
Force of friction = 343 N
Now, we can substitute the force of friction into Newton's second law:
F = m * a
343 N = 70 kg * a
To find the acceleration (a), divide both sides of the equation by the mass (70 kg):
a = 343 N / 70 kg
a ≈ 4.9 m/s^2
Therefore, the acceleration of the box is approximately 4.9 m/s^2.