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Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s. The top of this rise can be modeled as a circle of radius 4.1 m. The sled and occupant have a combined mass of 110 kg. If the coefficient of kinetic friction between the snow and the sled is 0.10, what friction force is exerted on the sled by the snow as the sled goes over the top of the rise? 1) 2) A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds. A person weighing 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (that is, the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion? 2) 3) A 600-kg car traveling at 24.5 m/s is going around a curve having a radius of 120 m that is banked at an angle of 20°. (a) Is the curve properly banked for the car's speed? (b) What is the minimum coefficient of static friction required between the road and the car's tires so the car does not skid? 3) 4) A time-varying horizontal force F(t) = At4 + Bt2 acts for 0.500 s on a 12.25-kg object, starting at time t = 1.00 s. In the SI system, A has the numerical value 4.50 and B has the numerical value 8.75. (a) What are the SI units of A and B? (b) What impulse does this force impart to the object? 4) 5) A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. Assume that any other unbalanced forces are negligible. (a) What is the speed of the wreckage just after the collision? (b) In what direction does the wreckage move just after the collision? 5) 6) A 2.50-kg stone is dropped from rest at a height of 3.75 m. What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground, assuming negligible air resistance? 6) 7) A 10.0-kg shell is traveling horizontally to the right at 25.0 m/s relative to the ground when it explodes into two fragments, one of mass 3.00 kg and the other of mass 7.00 kg. The lighter fragment goes directly forward, and the explosion releases 1.50 × 103 J of 7) 8) A force on an object is given by F(x) = (2.00 N/m)x - (3.00 N/m3 )x 3 . What is a potential energy function U(x) for this conservative force? 8) mechanical energy to the fragments. Find the magnitude and direction of the velocity of the heavier fragment relative to the ground just after the explosion. Ignore the effect of any ejected gases. 1 9) Three cars (car F, car G, and car H) are moving with the same velocity when the driver suddenly slams on the brakes, locking the wheels. The most massive car is car F, the least massive is car H, and all three cars have identical tires. (a) Which car travels the longest distance to skid to a stop? A) Car F B) Car G C) Car H D) They all travel the same distance in stopping. 9) (b) For which car does friction do the largest amount of work in stopping the car? A) Car F B) Car G C) Car H D) The amount of work done by friction is the same for all cars. 10) It requires 6.0 J of work is needed to push a 2.0-kg object from point A to point B of the frictionless ramp as shown in the figure. What is the length s of the ramp from A to B? 10) 11) In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1800 kg. Find the magnitude of the force of the car on the track when the car is at point A. You can treat the car as a point mass. 11) 12) When a particle is a distance r from the origin, its potential energy function is given by the equation U(r) = kr, where k is a constant and r = x 2 + y 2 + z2 12) (a) What are the SI units of k? (b) Find a mathematical expression in terms of x, y, and z for the y component of the force on the particle. (c) If U = 3.00 J when the particle is 2.00 m from the origin, find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m). 2 13) An object of mass 4.0 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in the figure. If the speed of the object at the bottom of the inclined plane is 10 m/s, how much work does friction do on this object as it slides down the incline? 13) 14) Two boys searching for buried treasure are standing underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree. 14) 15) A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m2 )x 2 15) If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m. ^ ^ ^ ^ ^ ^ 16) If A = 3i - j + 4k and B = xi + j - 5k , find x so B will be perpendicular to A . 16) 17) In the figure, a block of mass m is moving along the horizontal frictionless surface with a speed of 5.70 m/s. If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260, how far does the block travel up the incline? 17) 3 18) Three forces, F1 = 20.0 N, F2 = 40.0 N, and F3 = 10.0 N act on an object with a mass of 2.00 18) kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by (a) F1 (b) F2 (c) F3. 19) A 2.5-kg box, sliding on a rough horizontal surface, has a speed of 1.2 m/s when it makes contact with a spring (see the figure). The block comes to a momentary halt when the compression of the spring is 5.0 cm. The work done by the friction, from the instant the block makes contact with the spring until is comes to a momentary halt, is -0.50 J. 19) (a) What is the spring constant of the spring? (b) What is the coefficient of kinetic friction between the box and the rough surface? 20) An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves (a) from 4 m to 6 m? (b) from 6 m to 12 m? 4 20) Answer Key Testname: PRACTICETEST3 1) 88 N 2) 460 N 3) (a) No (b) 0.12 4) (a) A: N/s4 = kg · m/s6 , B: N/s2 = kg · m/s4 5) (a) 12.2 m/s (b) 48.0° N of E 6) 21.4 N · s 7) 13.7 m/s to the right 8) U(x) = (-1.00 N/m)x 2 + (0.750 N/m3 )x 4 9) (a) D (b) A 10) 0.61 m 11) 53,000 N 12) (a) kg · m/s2 (or J/m or N) (b) Fy = - (b) 12.9 N · s, horizontally ky x2 + y 2 + z2 (c) -0.802 N 13) -190 J 14) 15) 16) 17) 18) 19) 20) -90 m 2 20 m/s 7 3.72 m (a) 12.0 J (b) 20.8 J (c) 0.00 J (a) 1040 N/m (b) 0.41 (a) 20 J (b) 30 J 5