Question

Energy, Force, and Kinematics A smooth frictionless incline is d meters in length and is at an angle of theta > 30 degree with respect to the ground. A block of mass mA = m starts from rest at the top of the incline (see figure). It is connected to a lighter mass mB = m/2 by a massless string that stays taut throughout the block's descent. In terms of the given quantities m, theta , and acceleration due to gravity g answer the following questions. Figure 5: Sliding block Draw free body diagrams showing all the forces acting on each of the two blocks. Also write down the equation of motion (Newton's Second Law) for each of the two masses. What is the acceleration of the block mA down the incline? (Note that this is the same in magnitude as the acceleration of block mB) What is the tension in the string? What is the total work done by the net force (gravity and tension) on the block mA as it slides to the bottom of the incline? How does this compare with the work done by the net force on the block mB? What is the speed of the block mA at the bottom of the slide? (Hint: Use work-energy theorem and your answer to (d) above). How long does the block mA take to slide down the incline?

Answer 1