SYSTEMS (ADDING & SUBTRACTING ENERGY!) 6.1 TOBOGGANS ON HORIZONTAL-SPEED The figures to the right represent identical...
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SYSTEMS (ADDING & SUBTRACTING ENERGY!) 6.1 TOBOGGANS ON HORIZONTAL-SPEED The figures to the right represent identical toboggans that have traveled down a snowy hill. The toboggans all have the same speed at the bottom of the hill. Assume that the horizontal surfaces that they travel along are frictionless except for the shaded areas, where the coefficient of friction is given. These shaded areas have different lengths as shown. A Rank the speed of the toboggans as they reach point P. Greatest 1 2 3 4 Please justify your reasoning using an equation Least L= 0.5 P 6 m u = 0.4 P B u = 0.2 P D 3 m Case A -0.5 m 6.2 Two blocks are on a frictionless ramp and held against a spring that is compressed 0.50 m. (The mass of the blocks and force constant of the springs are given.) The blocks are then released from rest, and the compressed spring causes the blocks to accelerate up the ramp while in contact with the blocks. At the instant shown, the blocks are just about to lose contact with the end of the spring. Is the height that the block travels up the incline in Case A greater than, less than, or equal to the height that the block travels up the incline in Case B? Justify your reasoning. 1 N/m hmmmmm kg 7. A child (m=50 kg) starts from rest at the top of a 5.0-m long slide (vertical height =3.0 m) (a) If she reaches the bottom with a speed of 6.0 m/s, what was the average force of friction acting along the incline? Case B 1 N/m u=0.5 0.5 m 5 kg 5.0 m 3.0 m (b) Now consider the 3.0m high slide generally. Does velocity at the bottom depend on the angle of the hill... ...If there is no friction? YES NO ...If there is friction? YES NO (c) We are still on the slide theme (yeah!). However we go to a different, completely frictionless slide. A youngster starts from rest at the top, reaching the bottom with a speed of 12 m/s. On the next ride, her friend gives her a push so she leaves the top with a velocity of 5 m/s. With what speed does the rider now reach the bottom? Same slide, and again no friction. (a) 5 m/s (b) 12 m/s (c) 13 m/s (d) 17 m/s (Question 7.1, 7.2 Source: CJ Hieggelke, D P Maloney, and S E Kanim. nTIPERS:. Pearson. 2012.) SYSTEMS (ADDING & SUBTRACTING ENERGY!) 6.1 TOBOGGANS ON HORIZONTAL-SPEED The figures to the right represent identical toboggans that have traveled down a snowy hill. The toboggans all have the same speed at the bottom of the hill. Assume that the horizontal surfaces that they travel along are frictionless except for the shaded areas, where the coefficient of friction is given. These shaded areas have different lengths as shown. A Rank the speed of the toboggans as they reach point P. Greatest 1 2 3 4 Please justify your reasoning using an equation Least L= 0.5 P 6 m u = 0.4 P B u = 0.2 P D 3 m Case A -0.5 m 6.2 Two blocks are on a frictionless ramp and held against a spring that is compressed 0.50 m. (The mass of the blocks and force constant of the springs are given.) The blocks are then released from rest, and the compressed spring causes the blocks to accelerate up the ramp while in contact with the blocks. At the instant shown, the blocks are just about to lose contact with the end of the spring. Is the height that the block travels up the incline in Case A greater than, less than, or equal to the height that the block travels up the incline in Case B? Justify your reasoning. 1 N/m hmmmmm kg 7. A child (m=50 kg) starts from rest at the top of a 5.0-m long slide (vertical height =3.0 m) (a) If she reaches the bottom with a speed of 6.0 m/s, what was the average force of friction acting along the incline? Case B 1 N/m u=0.5 0.5 m 5 kg 5.0 m 3.0 m (b) Now consider the 3.0m high slide generally. Does velocity at the bottom depend on the angle of the hill... ...If there is no friction? YES NO ...If there is friction? YES NO (c) We are still on the slide theme (yeah!). However we go to a different, completely frictionless slide. A youngster starts from rest at the top, reaching the bottom with a speed of 12 m/s. On the next ride, her friend gives her a push so she leaves the top with a velocity of 5 m/s. With what speed does the rider now reach the bottom? Same slide, and again no friction. (a) 5 m/s (b) 12 m/s (c) 13 m/s (d) 17 m/s (Question 7.1, 7.2 Source: CJ Hieggelke, D P Maloney, and S E Kanim. nTIPERS:. Pearson. 2012.)
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