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# Force and Maximum Height

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Problems 9) A mechanic pushes a 2. 50103kg car from rest to a speed of v, doing 5000J of work in the process. During this time, the car moves 25. 0m. Neglecting friction between the car and road, find (a) v and (b) the horizontal force exerted on the car. 25) A daredevil on a motorcycle leaves the end of a ramp with a speed of 35. 0 m/s as in the figure P5. 25. If his speed is 33. 0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.

31) A horizontal spring attached to a wall has a force constant of 850 N/m.

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A block of mass 1. 00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in Active Figure 5. 20. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c ) Find the energy stored in the spring when the mass passes through the equilibrium and again when the mass passes through equilibrium after being released from rest.

d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium?

35) a 0. 250-kg block along a horizontal track has a speed of 1. 50 m/s immediately before colliding with a light spring of force constant 4. 60 N/m located at the end of the track. (a) What is the spring’s maximum compression if the track is frictionless? (b) If the track is not frictionless, would the spring’s maximum compression be greater that, less than or equal to the value obtained in part (a)? 36) A block of mass m=5. 0kg is released form point a and slides on the frictionless track shown in figure p5. 36. Determine (a) the bead’s speed at points b and c and (b) the net work done by the force of gravity in moving the bead from A to C. 37)Tarzan seeings on a 30. 0-m long vine initially inclined at an angle of 37. 0º with the vertical. What is his speed at the bottom of the swing (a ) if he starts from rest? (b) if he pushes off with a speed of 4. 00m/s? 39)The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5. 39a.

If the spring is compressed a distance of 0. 120m and the gun fired vertically as shown. the gun can launch a 20. 0-g projectile from rest to a maximum height of 20. 0m above the starting point of the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and © find the speed of the projectile as it moves through the equilibrium position of the spring (where x=0), as shown in figure p5. 39b. 41) (a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it.

Can the equation foe conservation of mechanical energy be used on the child? (b) Is the mass of the child a factor in determining his speed at the bottom of the slide? © The child drops straight down rather than following the curved ramp of the slide. In which case will he be modified? (e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 12. 0m. 56) A certain rain cloud at an altitude of 1. 75km contains 3. 20 107kg water vapor. How long would it take for a 2. 70-kW pump to raise the same amount of water from Earth’s surface to the cloud’s position?

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