A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal sur- face as in Figure P8.35. (a) The block is pulled to a posi- 6.00 cm fromn equilibrium and released. Find the clastic potential energy stored in the spring when the block is 6.00 cm from equilibrium and when the block passes through cquilibrium. (b) Find the speed of the block as it passes through the equilibrium point. (c) What is the speed of the block when it is at a position x/2= 3.00 cm? (d) Why isn't the answer to part (c) half the answer to part (b)? tion

A 7.80 g bullet is moving at 460 m/s just before it penetrates a tree trunk to a depth of 4.9 cm (ay What the magnitude of the average frletional force (In N) that is exerted on the bullet whille moving the tree trunk? Uso work considerations to o your answer. (b) Asturing the frictional force is constant, how much time elapses between the moment the bullet enters the tree trunk and the moment it moving?

Figure (a) applies to the spring in a cork gun (Figure (b)); it shows the spring force as a function of the stretch or compression of the spring. The spring is compressed by 7.00 cm and used to propel a 3.90 g cork from the gun. (a) What is the speed of the cork if it is released as the spring passes through its relaxed position? (b) Suppose, instead, that the cork sticks to the spring and stretches it 1.70 cm before separation occurs. What now is the speed of the cork at the time of release? Force (N) 0.4 0.2 -4-2 2 4 -0.2 -0.4 (a) x (cm) Compressed spring. 0 (b) Cork

A pendulum consists of a 1.2 kg stone swinging on a 4.2 m string of negligible mass. The stone has a speed of 8.3 m/s when it passes its lowest point. (a) What is the speed when the string is at 56" to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system? (a) Number i Unit (b) Number i Unit (c) Number i Unit

.  A pogo stick has a spring with a spring constant of 2.5×104N/m,, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?