A 3.0 kg block is moved up a 37 degree incline under a constant horizontal force of 40.0 N. The coefficient of friction is 0.10 and the block is displaced 2.0 m up the incline. Calculate the change in the kinetic energy of the block.
Work is done on the block therefore kinetic energy is 1/2mv^2.
Identify the object - Block
Win or Wo = F*d
KEi or Keo = 1/2mv^2
Pei or Peo = mgh
Wf = coefficient of friction
-Is work done on the block from the start= Yes = Work in
-Is the object moving at the beginning = yes = Kei
-Is the object at a certain height or is it storing energy elastically - yes = Pei
-Is work done by the object - No (this would be work out or Wo)
-Is there work done against friction due to restive loss - Yes = Wf
-Is the object moving at the end - no (this would be Ke out)
-Is the object at a certain height or is it storing energy elastically at the end - No = Peo
-Does the object consume fuel - No - (This would be Ui)
So your equation would start off as Wi + Pei + Kei = Wf
Rearrange in Algebraic terms to determine Ke
To calculate the change in the kinetic energy of the block, we need to determine the initial and final velocities of the block.
First, let's find the net force acting on the block along the incline. We know that there is a horizontal force of 40.0 N, and the block is on an incline of 37 degrees with respect to the horizontal.
The component of the force acting parallel to the incline is given by the equation: F_parallel = F_applied * sin(θ), where θ is the angle of the incline. Substituting the values, we get: F_parallel = 40.0 N * sin(37°).
Next, we need to calculate the force of friction acting on the block. The frictional force can be calculated using the equation: F_friction = μ * F_normal, where μ is the coefficient of friction, and F_normal is the normal force. The normal force acting on the block is equal to the weight of the block, which can be calculated as: F_normal = m * g, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).
Now, let's find the force of friction by substituting the values: F_friction = 0.10 * (3.0 kg * 9.8 m/s^2).
Since the block is moving up the incline, the net force can be determined as: F_net = F_parallel - F_friction.
Next, we can calculate the acceleration of the block using Newton's second law: F_net = m * a, where m is the mass of the block. We can rearrange the equation to solve for acceleration: a = F_net / m.
Now, we know the initial velocity of the block is 0 m/s since it starts from rest. Using the equation of motion: v_final^2 = v_initial^2 + 2 * a * d, we can find the final velocity of the block. Here, d represents the displacement of the block up the incline, which is given as 2.0 m.
Once we have the initial and final velocities, we can calculate the change in kinetic energy using the equation: ΔKE = (1/2) * m * (v_final^2 - v_initial^2).
By following these steps, you can find the change in the kinetic energy of the block.