1) A 0.280-kg block along a horizontal track has a speed of 1.40 m/s immediately before colliding with a light spring of force constant 5.00 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 than, less than, or equal to the value obtained in part (a)? greater less equal

2) A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (see figure). She is launched from a height h/5 into the pool.

An illustration shows a child sliding down a curved slide next to a swimming pool. The slide has a horizontal rest at the top, at the height of h from the ground. The slide then has a steep dip down to the ground, where it curves again and goes upward to a height h/5 and ends there. The child is shown as being launched from this height into the air over the pool. The parabolic path the child takes through the air starts at an angle with the horizontal. The maximum height of this path above the water is labeled ymax. (a) Is mechanical energy conserved? Yes No

Why? b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (Use the following as necessary: height h, mass m, and gravitational acceleration g.) potential energy kinetic energy launching point in the pool (c) Determine her initial speed v0 at the launch point in terms of g and h. v0 = (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. ymax = (e) Use the x-component of the answer to part (c) to eliminate v0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle . ymax = (f) Would your answers be the same if the waterslide were not frictionless? Yes No

Explain.

3) When an automobile moves with constant speed down a highway, most of the power developed by the engine is used to compensate for the mechanical energy loss due to frictional forces exerted on the car by the air and the road. If the power developed by the engine is 167 hp, estimate the total friction force acting on the car when it is moving at a speed of 34 m/s. One horsepower equals 746 W.

4)A 1.50 10³-kg car starts from rest and accelerates uniformly to 19.3 m/s in 12.9 s. Assume that air resistance remains constant at 400 N during this time.

(a) Find the average power developed by the engine. (b) Find the instantaneous power output of the engine at t = 12.9 s, just before the car stops accelerating. 5) The force acting on a particle varies as in the figure below. (Thexaxis is marked in increments of2.50m.)A coordinate plane has a horizontal axis labeledx(m)and a vertical axis labeledF_x(N). There are five points, connected by straight lines in order from A to E.

• Point A is at (0,0).
• Point B is at (10,6).
• Point C is at (20,0).
• Point D is at (25,3).
• Point E is at (30,0).

Find the work done by the force as the particle moves across the following distances.

(a) from x= 0 m to x=20.0m

(b) from x=20.0m to x=30.0m

(c) from x= 0 m to x=30.0m