Final answer:
To determine the tension P in the cable to give the 100-lb block a steady acceleration of 5 ft/sec^2 up the incline, you need to consider the forces acting on the block. The tension in the cable is equal to the weight of the block plus the product of its mass and acceleration. Plugging in the values, the tension comes out to be approximately 100.5 lb.
Step-by-step explanation:
To determine the tension P in the cable to give the 100-lb block a steady acceleration of 5 ft/sec^2 up the incline, we need to consider the forces acting on the block. The weight of the block is equal to its mass times the acceleration due to gravity, which is 32 ft/sec^2. This downward force is counteracted by the tension in the cable. So, we can set up the following equation: Tension = Weight + (Mass x Acceleration).
In this case, the weight of the block is 100 lb, which is equivalent to 100/32 = 3.125 slugs (1 slug = 32.2 lb ft/sec^2). The mass of the block is then 3.125/32.2 ≈ 0.097 kg.
Using the equation Tension = Weight + (Mass x Acceleration), Tension = 100 + (0.097 x 5) = 100 + 0.485 ≈ 100.5 lb.