A 20.0 kg box slides down a 12.0 m long incline at an angle of 3.0 degrees with the horizontal. A force of 50.0 N is applied to the box to try to pull it up the incline. The applied force makes an angle of 0.00 degrees to the incline. If the incline has a coefficient of kinetic friction of 0.100, then the increase in the kinetic energy of the box is
593j
its wrong!!!!!!
M*g = 20 * 9.8 = 196 N. = Wt. of box.
Fp = 196*sin3 = 10.26 N. = Force parallel to the incline.
Fn = 196*Cos3 = 195.7 N. = Force perpendicular to the incline.
Fk = u*Fn = 0.1 * 195.7 = 19.57 N. = Force of kinetic friction.
a = (Fap-Fp-Fk)/M = (50-10.26-19.57)/20 =1.01 m/s^2
V^2 = Vo^2 + 2a*d = 0 + 2.02*12 = 24.24
V = 4.92 m/s.
KE = 0.5*20*4.92^2 = 242 J.
To find the increase in the kinetic energy of the box, we need to calculate the work done on the box.
The work done on an object can be calculated using the formula:
Work = Force × Distance × cos(θ),
where
- "Force" is the applied force (50.0 N),
- "Distance" is the distance the box moves along the incline (12.0 m), and
- "θ" is the angle between the applied force and the incline (0.00 degrees).
First, let's calculate the component of the applied force parallel to the incline. Since the applied force is perpendicular to the incline, the component of the applied force parallel to the incline is given by:
Force_parallel = Force × sin(θ),
where "θ" is the angle between the incline and the horizontal (3.0 degrees in this case).
Now, let's calculate the force of gravity acting down the incline. The force of gravity can be calculated using the formula:
Force_gravity = mass × acceleration due to gravity,
where
- "mass" is the mass of the box (20.0 kg),
- "acceleration due to gravity" is approximately 9.8 m/s^2.
The force of friction acting on the box is given by:
Force_friction = coefficient of kinetic friction × force normal,
where
- "coefficient of kinetic friction" is given as 0.100,
- "force normal" is the normal force acting on the box.
The normal force can be calculated using the formula:
Force_normal = mass × acceleration due to gravity × cos(θ),
where "θ" is the angle between the incline and the horizontal (3.0 degrees).
Next, let's calculate the net force acting on the box. The net force is the difference between the force parallel to the incline and the force of friction:
Net_force = Force_parallel - Force_friction.
Finally, we can calculate the work done on the box using the formula mentioned earlier:
Work = Net_force × Distance × cos(θ).
The increase in the kinetic energy of the box is equal to the work done on the box.
Now, let's calculate the values and plug them into the formulas to find the increase in the kinetic energy of the box.