The coefficients of static and kinetic friction between a 50 kg box and a horizontal surface are 0.64 and 0.17, respectively. What is the acceleration of the object if a 335 N horizontal force is applied to the box?
To find the acceleration of the object, we need to consider the forces acting on it. In this case, we have the applied force, the force of friction, and the weight of the box.
The force of friction can be determined using the formula:
Frictional Force = Coefficient of Friction * Normal Force
The normal force is equal to the weight of the object, which can be calculated as:
Weight = mass * gravitational acceleration
Plugging in the given values:
Weight = 50 kg * 9.8 m/s^2 = 490 N
Now let's calculate the force of friction:
Static Friction = 0.64 * 490 N = 313.6 N
Kinetic Friction = 0.17 * 490 N = 83.3 N
Since the applied force (335 N) is greater than the maximum static friction (313.6 N), the box will move, and we need to consider the kinetic friction.
Now, let's calculate the net force:
Net Force = Applied Force - Force of Kinetic Friction
= 335 N - 83.3 N
= 251.7 N
Finally, we can calculate the acceleration using Newton's second law of motion:
Net Force = mass * acceleration
Rearranging the equation:
acceleration = Net Force / mass
Plugging in the values:
acceleration = 251.7 N / 50 kg
= 5.03 m/s^2
Therefore, the acceleration of the object is 5.03 m/s^2.