An 82.9 N box of clothes is pulled 28.2 m up
a 20.7◦
ramp by a force of 117 N that points
along the ramp.
The acceleration of gravity is 9.81 m/s^2.
If the coefficient of kinetic friction between the box and ramp is 0.29, calculate the change
in the box’s kinetic energy.
Answer in units of J
To calculate the change in the box's kinetic energy, we need to find the work done on the box by all the forces acting on it. The work done is equal to the change in kinetic energy.
First, let's find the work done by the force that is pulling the box up the ramp. The work done by a force is equal to the magnitude of the force multiplied by the displacement in the direction of the force. In this case, the force applied is 117 N, and the displacement is 28.2 m. Since the force is acting along the ramp, we need to decompose it into two components: one parallel to the displacement and one perpendicular to the displacement.
The parallel component of the force is given by F_parallel = F * sin(θ), where θ is the angle between the force and the displacement. In this case, θ = 20.7°. So the parallel component is F_parallel = 117 N * sin(20.7°).
Now, let's calculate the work done by this component of the force. The work done is given by W_parallel = F_parallel * displacement.
Next, let's find the work done by the force of friction. The force of friction is given by F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force. Since the box is being pulled up the ramp, the normal force is equal to the weight of the box, which is given by F_normal = m * g, where m is the mass of the box and g is the acceleration due to gravity. In this case, the weight of the box is 82.9 N.
Now, let's calculate the force of friction. F_friction = 0.29 * F_normal.
Finally, let's calculate the work done by the force of friction. The work done is given by W_friction = F_friction * displacement.
The total work done on the box is equal to the sum of the work done by the force that is pulling it up the ramp and the work done by the force of friction. The change in kinetic energy is equal to the total work done.
So, the change in kinetic energy = W_parallel + W_friction.
Now, you can substitute the values into the equations and calculate the change in kinetic energy.