Two blocks, A and B (with mass 50 kg and 100 kg, respectively), are connected by a string, as shown in Figure P5.64. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is µk = 0.25. Determine the change in the kinetic energy of block A as it moves from C to D, a distance of 19 m up the incline if the system starts from rest.
Angle is 37
So far all I have is Fk = 97.8N
Appreciate it!
To determine the change in the kinetic energy of block A as it moves from point C to point D, we can follow these steps:
Step 1: Calculate the force of gravity acting on each block.
The force of gravity on block A (FgA) can be calculated using the formula Fg = m * g, where m is the mass of the block and g is the acceleration due to gravity. In this case, m = 50 kg and g ≈ 9.8 m/s². Therefore, FgA = 50 kg * 9.8 m/s² = 490 N.
Similarly, the force of gravity on block B (FgB) can be calculated as FgB = 100 kg * 9.8 m/s² = 980 N.
Step 2: Calculate the force of friction acting on block A.
The force of kinetic friction (Fk) acting on block A can be determined using the formula Fk = µk * N, where µk is the coefficient of kinetic friction and N is the normal force. In this case, µk = 0.25.
The normal force (N) can be calculated using the formula N = FgA * cos(θ), where θ is the angle of the incline. In this case, the angle is given as 37°.
N = 490 N * cos(37°) ≈ 390.60 N.
Therefore, Fk = 0.25 * 390.60 N ≈ 97.65 N.
Step 3: Calculate the net force acting on block A.
The net force (Fnet) acting on block A can be determined by subtracting the force of friction (Fk) from the component of the force of gravity parallel to the incline (Fgp), which is given by Fgp = FgA * sin(θ).
Fgp = 490 N * sin(37°) ≈ 293.88 N.
Therefore, Fnet = Fgp - Fk = 293.88 N - 97.65 N = 196.23 N.
Step 4: Calculate the work done on block A.
The work done on block A (W) can be calculated using the formula W = Fnet * d, where d is the distance traveled by the block. In this case, the distance is given as 19 m.
Therefore, W = 196.23 N * 19 m = 3728.37 J (joules).
Step 5: Calculate the change in kinetic energy of block A.
The change in kinetic energy (∆KE) of block A can be calculated using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
Therefore, ∆KE = W = 3728.37 J.
Hence, the change in the kinetic energy of block A as it moves from point C to point D along the incline is approximately 3728.37 Joules.