# Physics Homework #5

1. In the figure, a slide-loving pig slides down a certain 38° slide in twice the time it would take to slide down a frictionless 38° slide. What is the coefficient of kinetic friction between the pig and the slide? 2. Flying Circus of physics
The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if they had been migrating (see the figure). For years curiosity mounted about why the stones moved. One explanation was that strong winds during the occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.751. What horizontal force is needed on a stone of typical mass 14 kg to maintain the stone’s motion once a gust has started it moving?
103.04 Units: N

3. A worker pushes horizontally on a 38.0 kg crate with a force of magnitude 114 N. The coefficient of static friction between the crate and the floor is 0.390. (a) What is the value offs,max under the circumstances? (b) Does the crate move? (“yes” or “no”) (c) What is the frictional force fr on the crate from the floor? (d) Suppose, next, that a second worker pulls directly upward on the crate to help out. What is the least vertical pull fpv that will allow the first worker’s 114 N push to move the crate? (e) If, instead, the second worker pulls horizontally to help out, what is the least pull fpg that will get the crate moving? 4. The figure shows the cross section of a road cut into the side of a mountain. The solid line AA′ represents a weak bedding plane along which sliding is possible. Block B directly above the highway is separated from uphill rock by a large crack (called a joint), so that only friction between the block and the bedding plane prevents sliding. The mass of the block is 3.4 × 107kg, the dip angle θ of the bedding plane is 29°, and the coefficient of static friction between block and plane is 0.65. (a) Will the block slide under these circumstances? (“yes” or “no”)(b) Next, water seeps into the joint and expands upon freezing, exerting on the block a force parallel to AA′. What minimum value of F will trigger a slide down the plane? 5. A block is pushed across a floor by a constant force that is applied at a downward angle θ, as shown in the first figure here. The second figure gives the acceleration of the block versus the coefficient of kinetic friction μk between block and floor: a1 = 2.9 m/s2, μk2 = 0.30, and μk3 = 0.60. What is the value of θ? 6. Continuation of Problem 8: The mysterious sliding stones. Along the remote Racetrack Playa in Death Valley, California, stones sometimes gouge out prominent trails in the desert floor, as if the stones had been migrating (see the figure). For years curiosity mounted about why the stones moved. One explanation was that strong winds during occasional rainstorms would drag the rough stones over ground softened by rain. When the desert dried out, the trails behind the stones were hard-baked in place. According to measurements, the coefficient of kinetic friction between the stones and the wet playa ground is about 0.74.
Now assume that equation gives the magnitude of the air drag force on a typical 19 kg stone, which presents to the wind a vertical cross-sectional area of 0.040 m2and has a drag coefficient C of 0.76. Take the air density to be 1.21 kg/m3. (a) What wind speed V along the ground is needed to maintain the stone’s motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of 10 m. Assume wind speeds are 2.1 times those along the ground. (b) For your answer to (a), what wind speed would be reported for the storm? (Story continues with Problem 65.) 7. A circular-motion addict of mass 83.0 kg rides a Ferris wheel around in a vertical circle of radius 13.0 m at a constant speed of 8.10 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?
a. 10.08 Units: s b. 394.51 Units: N c. 1248.89 Units: N

8. In the figure, a box of ant aunts (total mass m1 = 1.20 kg) and a box of ant uncles (total mass m2 = 3.85 kg) slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is θ = 26°. The coefficient of kinetic friction between the aunt box and the incline is μ1 = 0.208; that between the uncle box and the incline is μ2 = 0.140. Compute (a) the tension in the rod and (b) the common acceleration of the two boxes. a. 0.55 Units: N b. 2.92 Units: m/s^2

9. In the figure, a 49 kg rock climber is climbing a “chimney” between two rock slabs. The coefficient of static friction between her shoes and the rock is 1.18; between her back and the rock it is 0.709. She has reduced her push against the rock until her back and her shoes are on the verge of slipping. (a) What is the magnitude of each of her forces of push against the two columns of rock? (b) What fraction of her weight is supported by the frictional force on her shoes? 10. A house is built on the top of a hill with a nearby slope at angle θ = 49° (see the figure). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the static coefficient of friction between two such layers is 0.66, what is the least angle φ through which the present slope should be reduced to prevent slippage? 