An 66.0 N box of clothes is pulled 5.5 m up a 30.0° ramp by a force of 116 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.
To calculate the change in the box's kinetic energy, we need to find the work done on the box.
First, let's break down the forces acting on the box as it is being pulled up the ramp.
1. Force of gravity: The box has a weight of 66.0 N acting vertically downward.
2. Normal force: The ramp exerts a normal force perpendicular to the surface, which balances the box's weight.
3. Force of friction: Since the coefficient of kinetic friction is given, we can calculate the force of friction using the equation F_friction = coefficient of kinetic friction * normal force.
Next, let's find the net force acting on the box by resolving the force along the direction of motion.
1. Force parallel to the ramp: This is the force being applied along the ramp, which is 116 N in this case.
2. Force of gravity along the ramp: This force can be found by multiplying the weight of the box by the sine of the angle of the ramp, since the force acting parallel to the ramp is only a component of the box's weight.
Now that we have the net force acting on the box, we can find the work done.
1. Work done by the applied force: This force is acting in the direction of motion and can be calculated using the equation Work = Force * Distance * cos(angle), where the angle is the angle between the force and the direction of motion.
2. Work done against friction force: This force is acting in the opposite direction of motion and can be calculated using the equation Work = Force * Distance (since the force and the displacement are in the same direction).
Finally, the change in kinetic energy is equal to the work done on the box.
1. Change in kinetic energy = Work done by applied force + Work done against friction force.
By substituting the given values into the equations and calculations, you can find the change in the box's kinetic energy.
h = L*sin A = 5.5*sin30 = 2.75 m.
Fn = mg*Cos A = 66*Cos 30 = 57.16 N. =
Normal force = Force perpendicular to
the ramp.
Fk = u*Fn = 0.22 * 57.16 = 12.57 N. =
Force of kinetic friction.
KE + PE = mg*hmax-Fk*L
KE + PE = 66*2.75-12.57*5.5 = 112.4 J.
0 + PE = 112.4
PE = 112.4 J. at bottom of ramp.
KE + PE = 112.4 J. at top of ramp.
KE + 0 = 112.4
KE = 112.4 J.
KE(change) = 112.4 - 0 = 112.4 J.