1. It takes a minimum distance of 98.26 m to stop a car moving at 17.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 26.0 m/s

2. A moving 3.10 kg block collides with a horizontal spring whose spring constant is 415 N/m

2.1. The block compresses the spring a maximum distance of 4.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.490. What is the work done by the spring in bringing the block to rest?

2.2. How much mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring?

2.3. What is the speed of the block when it hits the spring?

3. A constant force of 31.9 N, directed at 26.9 from horizontal, pulls a mass of 13.9 kg horizontally a distance of 2.93 m. Calculate the work done by the force.

4. Calculate the change in potential energy of a 88.9 kg man when he takes an elevator from the first floor to 39th floor, if the distance between floors is 4.05 m

5. The rope of a swing is 3.30 m long. Calculate the angle from the vertical at which a 83.0 kg man must begin to swing in order to have the same KE at the bottom as a 1480 kg car moving at 1.49 m/s (3.33 mph).

6. A 33.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 21.00 m. When she is partway down the slide, at a height h2 of 10.00 m, she is moving at a speed of 7.70 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).

7. A 2.50 kg box slides down a rough incline plane from a height h of 1.99 m. The box had a speed of 3.21 m/s at the top and a speed of 2.78 m/s at the bottom. Calculate the mechanical energy lost due to friction (as heat, etc.).

8. When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 2.01 m/s. The mass stops a distance S2 = 1.9 m along the level part of the slide. The distance S1 = 1.07 m and the angle ? = 37.30. Calculate the coefficient of kinetic friction for the mass on the surface.

9. A car (m = 680.0 kg) accelerates uniformly from rest up an inclined road which rises uniformly, to a height, h = 31.0 m. Find the average power the engine must deliver to reach a speed of 23.3 m/s at the top of the hill in 15.3 s(NEGLECT frictional losses: air and rolling, ...)

\fNonk done by spring force : wonk done 2.1 Comprussion W = - ixx ox TIM 2=0 to x = a = 40'm - - 3kx2 = - 2X 415 x (0.04) 2 .: K = 415 N/m 21 = 40m = 0.04 m Ws = - 0' 332 Joule Ans. . : wonk done by spring is negative while it compressed. 22 .2 mechanical energy dissipated = wonk done by friction . : block is moving toward night so friction will act towards left AN : Nang ) Wools done by frictional force = - ve ( FR 2 2( antipenalul) my .: FK = MANY = NKmg - - MKmax = 0.490 X 3.10 X 9 . 8x (0:04) =0.595 5 OR = -0. 60 J - vesign (shows emergy is dissipates.\f3 hit us initialspeed of block ce ( striking speed ) final speed ZO (becomes comes at just Applying cons world- Energy theorem We + Wne + Wo = AKE 2 2 = =Kx + umgic = 0' 33 2 + 0 . 595 = 0.9272X0. 927 3. 10 1 = 0.771 m/s OR 0: 77 mis OR 77.1 em/s Which is initial speed of mass i's shaniksing speed.Hence, work done by spring force always negative because direction of displacement and spring force antipanallel to each other . Work done by spring Compression 2 100 0 0 0 00 ! Spring Force ( FS ) Edx Cos ( 180 ) e - - .: magnitude of Ws = - SKx2 Spring force | FS) = Kx similarly, work done by friction also negative because frictional force always act opposite direction to the motion of body ine . Friction fi.(4) " : Potential energy is given by us mah where h= height from Reference point . U = 68.9 x 9. 8x ( 39X 4.05 ) J = 13 7 60. 9 . 199 J U = 1 . 376 x 105 J Ans' Correct Answer for PE of man! (in 4 significant figure. U = 1.376 x 185 5 OR 1 . 38 X 105 5 Ans' ( After rounding fig ) 140te! .:4:05 for each floor, So For 39th flood total height h = 39 * 4:05 = 157.95 m,(7) mechanical energy lost all to the friction . work done by the friction Applying work- Energy Theorem We + wne + Wo = AK mgsine (0 . 341 + 9:31) MK = 8.374 -> MK = 8:374 ( 8.341 + 9.31 ) = 0. 474 i . e . coefficient of kinetic friction on Sunface MK = 0. 474 Ans Note: Here , we take both surface are rough and theirs frictional coefficient are equal