You exert a force of 200 N at an angle of 15 degrees above horizontal to pull a 10 kg box across the floor at constant velocity. If the coefficient of kinetic friction between the box and the floor is 0.42, what is the acceleration of the box?
some of the force is reducing weight W.
net force=mass*acceleration
200cos15-mu*W=m*acceleration
200cos15-mu*(mg-200sin15)=m*a
solve for acceleration a.
To find the acceleration of the box, we can first calculate the net force acting on the box.
The force you exert on the box can be split into two components: one parallel to the floor (horizontal component) and one perpendicular to the floor (vertical component). The vertical component does not affect the horizontal motion of the box since it is perpendicular to it, so we can focus on the horizontal component.
The horizontal component of the force you exert can be found using trigonometry. The formula to calculate it is:
Horizontal component = Applied force * cos(angle)
Given that the applied force is 200 N and the angle is 15 degrees, we can calculate the horizontal component as follows:
Horizontal component = 200 N * cos(15 degrees)
≈ 200 N * 0.9659
≈ 193.18 N
Now, let's calculate the force of kinetic friction acting on the box. The formula to calculate it is:
Force of kinetic friction = Coefficient of kinetic friction * Normal force
The normal force is equal to the weight of the box, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the box has a mass of 10 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight as follows:
Weight = 10 kg * 9.8 m/s²
= 98 N
Now, we can find the force of kinetic friction as:
Force of kinetic friction = 0.42 * 98 N
≈ 41.16 N
Since the box is moving at a constant velocity, the net force on the box must be zero. Therefore, the net force is equal to the force of kinetic friction. We can set up the equation:
Net force = Applied force - Force of kinetic friction
Since the net force is zero, we have:
0 = 193.18 N - 41.16 N
Now, we can solve for the acceleration of the box:
Acceleration = Net force / mass
Acceleration = 0 / 10 kg
= 0 m/s²
Therefore, the acceleration of the box is 0 m/s².