(III) A child slides down a slide with a 34° incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

A mass of 2.1 kg is dropped from a height of 4.4 meters above a vertical spring anchored at its lower end to the floor. If the spring constant is 22 N/cm, calculate how far (in cm), the spring is compressed.

(1) A 1200 kg roller coaster cart is initially at rest at the top of the track at a height of 20 m above ground. (a) What is the speed of the roller coaster when it reached ground level? (assume no friction in this part of the track). (b) The roller coaster now continues to move horizontally. Find the distance the roller coaster will travel before arriving at a complete stop, if the coefficient of friction between the coaster and the track is 0.3.

AT an accident scene on a level road, investigators measure a car's slid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be .30. (a) Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (b) Why does the car's mass not matter? (c) What is wrong with a car that skids?

A factory worker accidentally releases a 180 kg crate that was being held at rest at the top of a ramp that is 3.7 m long and inclined at 39 to the horizontal.The coefficient of kinetic friction between the crate and the ramp, and between the crate and the horizontal factory floor, is 0.28. (a) How fast is the crate moving as it reaches the bottom of the ramp? (b) How far will it subsequently slide across the floor? (Assume that the crate’s kinetic energy does not change as it moves from the ramp onto the floor.) (c) Do the answers to (a) and (b) increase, decrease, or remain the same if we halve the mass of the crate?

13–90. The 40-kg boy is sliding down the smooth spiral slide such that z = -2 m/s and his speed is 2 m/s. Determine the r, 0, z components of force the slide exerts on him at this instant. Neglect the size of the boy. r = 1.5 m

(III) A block of mass m is attached to the end of a spring (spring stiffness constant k), Fig. 6–43. The mass is given an initial displacement xo from equilibrium, and an initial speed vp. Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities. FIGURE 6–43 Problem 44.

(2) Four dollies (A, B, C and D) on a plane are connected by three ropes, ropes 1, 2 and 3, as shown in the diagram. The rightmost dolly is powered and pulled in the overall rightward direction by a force of magnitude F. The 4 dollies accelerate with the same acceleration. The friction between the ground and the dolly is negligible. At this point, answer the following questions. The rope does not stretch and the mass of the rope is neglected.< 台車D m4 ロープ3 m3 台車C ロープ2 m2 台車B ロープ1 m1 台車A F At this point, increase the strength of the F. Which rope breaks first. The ropes are all of the same strength.< (3) With all four trolleys of the same mass m, establish the equation of motion for each trolley in the right-hand direction of the paper. The right direction of the paper is the x- direction and only the equation of motion in the x-direction is derived. Also, include the tension of the rope between A and B as the tension of the rope between B and C and the tension of the rope between C and…

(a) How high (in m) a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 90.0 km/h?  ____________ m (b) If, in actuality, a 750 kg car with an initial speed of 90.0 km/h is observed to coast up a hill to a height 17.0 m above its starting point, how much thermal energy (in J) was generated by friction? (Enter a number.) ____________ J (c) What is the average force of friction (down the slope) if the hill has a slope 2.5° above the horizontal? (Enter your answer in N. Enter a number.) ____________ N