If there is now a constant air resistance force of 35 N, what is the new maximum height the ball attains?

Transcription

1 A 1kg ball is launched straight up into the air with an initial speed of 64 m/s. Using only energy considerations, determine the maximum height the ball attains assuming there is no air resistance. If there is now a constant air resistance force of 35 N, what is the new maximum height the ball attains? Problem 1

2 The ball launcher in a pinball machine has a spring with a force constant of 100 N/m. The surface on which the ball moves is inclined 10.0 with respect to the horizontal. If the spring is initially compressed 2.00 cm, find the launching speed of a kg ball when the plunger is released. Friction and the mass of the plunger are negligible. Problem 2

3 The koala bear is sliding down a 27 degree frictionless hill. If he starts from rest and slides 10 m: a) how fast is he going at the bottom? b) if he is given a push of 4 m/s in the beginning, how fast is he going now? c) If the hill now has a coefficient of friction of 0.3, how fast is he going if he started from rest? Problem 3

4 Problem 4

5 m = 5 kg k = 350 N/m x = 0.25 m = 0.08 AB = 0.25 m (a) Find the speed of the block after it passes AB once. (b) How far does the right spring compress after one pass. (c) How many times it will traverse AB? Problem 5

6 Problem 6

7 A B Assume M = 500 kg g = 10 m/s 2 D E A = 50 m B = 85 m C = 25 m D = 45 m E = 75 m F = 20 m C F (a) What initial speed is needed to make it over B? (b) If the car was pulled up over the 50 m distance instead, how much work would need to be done, and what would the minimum average force be to pull it? (c) How fast is the car going at all the points? (d) If the length of the track is 540 m from B to E, what is the maximum average frictional force that can exist if the car makes it through the loop? Problem 7

8 Problem 8

9 INELASTIC COLLISION WITH ENERGY LOSS Block A collides with Block B in a completely in elastic collision (stick together). Block A has a mass of 7 kg and was moving with a velocity of 22 m/s. Block B has a mass of 8 kg and was moving with a velocity of 5 m/s. Determine the velocity of the objects after the collision and determine the percent of energy lost in the collision. Problem 9

10 ELASTIC COLLISION Two balls collide elastically. Ball A has a mass of 5 kg and is moving with a velocity of 3 m/s. Ball B has a mass of 7 kg, and is moving at a velocity of 5 m/s. Determine the velocity of each ball after their elastic collision. Problem 10

11 A spring with a spring constant k is hung vertically. A mass m is gently attached to it and released in such a way that the spring is un-stretched upon release. The mass descends to a maximum spring extension X. Answer to following in terms of m, k, and g. (a) Determine X. (b) Determine the speed of the mass then the spring has stretched ¼ X, where the spring has stretched ¼ of its maximum extension X. (c) Determine the maximum speed of the mass (think when that will happen first). Problem 11

12 A mass m is dropped from a height H onto a hard, flat surface. When it collides with the surface, it rebounds with the same speed it had before the collision. However, there is a constant force of air resistance f acting on the mass as it undergoes this motion. Answer the following in terms of f, m, H, and g. (a) How fast is the mass moving just before it hits for the first time (don t forget air resistance)? (b) How high does the mass go after the first collision? (c) After many bounces, the ball comes to rest on the surface. While it overall displacement was H, it traveled a considerable larger distance. Determine the total distance traveled by the ball. Problem 12