Two blocks, A and B (with mass 50 kg and 100 kg, respectively), are connected by a string, as shown in Figure P5.63. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is µk = 0.23. Determine the change in the kinetic energy of block A as it moves from C to D, a distance of 15 m up the incline if the system starts from rest.
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To determine the change in kinetic energy of block A as it moves from point C to point D, we need to calculate the work done on block A and use the work-energy theorem.
1. Calculate the work done by the tension force on block A:
- The tension force, T, can be determined using the equation T = m * g * sin(θ), where m is the mass of block A (50 kg), g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline.
2. Calculate the work done by the force of kinetic friction on block A:
- The force of kinetic friction, fk, can be determined using the equation fk = µk * N, where µk is the coefficient of kinetic friction (0.23) and N is the normal force applied by the incline.
- The normal force can be calculated using the equation N = m * g * cos(θ), where m is the mass of block A and g is the acceleration due to gravity.
3. Calculate the net work done on block A:
- The net work done is given by the equation W_net = W_tension - W_friction, where W_tension is the work done by the tension force and W_friction is the work done by the force of kinetic friction.
4. Calculate the change in kinetic energy:
- The work-energy theorem states that the change in kinetic energy is equal to the net work done on the object. Therefore, ΔKE = W_net.
Now let's plug in the numbers and calculate:
1. Calculate Tension:
T = m * g * sin(θ)
T = 50 kg * 9.8 m/s^2 * sin(θ)
2. Calculate Normal force:
N = m * g * cos(θ)
N = 50 kg * 9.8 m/s^2 * cos(θ)
3. Calculate Friction force:
fk = µk * N
4. Calculate the work done by the tension force:
W_tension = T * distance (15m)
5. Calculate the work done by the force of kinetic friction:
W_friction = fk * distance (15m)
6. Calculate the net work done on block A:
W_net = W_tension - W_friction
7. Calculate the change in kinetic energy:
ΔKE = W_net
By following these steps and plugging in the values provided, the change in kinetic energy of block A as it moves from point C to D can be determined.