1. In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 × 10–11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 × 10–11 m. What are the (a) x and (b) y coordinates of the molecule’s center of mass?
2. A 1200 kg automobile is at rest at a traffic signal. At the instant the light turns green, the automobile starts to move with a constant acceleration of 2.6 m/s2. At the same instant a1850 kg truck, traveling at a constant speed of 6.4 m/s, overtakes and passes the automobile. (a) How far is the center of mass of the automobile-truck system from the traffic light att = 4.1 s? (b) What is the speed of the center of mass of the automobile-truck system then?
a. 24.514 Units: m
b. 8.052 Units: m/s
3. Two skaters, one with mass 58 kg and the other with mass 46 kg, stand on an ice rink holding a pole of length 13 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 46 kg skater move?
7.25 Units: m
4. Ricardo, of mass 84 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 40 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 2.9 m apart and symmetrically located with respect to the canoe’s center. Ricardo notices that the canoe moves 26 cm horizontally relative to a pier post during the exchange and calculates Carmelita’s mass. What is it?
66.89 Units: kg
5. The figure gives an overhead view of the path taken by a 0.170 kg cue ball as it bounces from a rail of a pool table. The ball’s initial speed is 1.17 m/s, and the angle θ1 is 60.8°. The bounce reverses the y component of the ball’s velocity but does not alter the x component. What are (a) angle θ2 and (b) the magnitude of the change in the ball’s linear momentum? (The fact that the ball rolls is irrelevant to the problem.)
a. 60.8 Units: degrees
b. 0.194 Units: kg*m/s or N*s
6. Two average forces. A steady stream of 0.264 kg snowballs is shot perpendicularly into a wall at a speed of 3.20 m/s. Each ball sticks to the wall. The figure gives the magnitude F of the force on the wall as a function of time t for two of the snowball impacts. Impacts occur with a repetition time interval Δtr = 45.0 ms, last a duration time interval Δtd = 13.0 ms, and produce isosceles triangles on the graph, with each impact reaching a force maximum Fmax = 130 N. During each impact, what are the magnitudes of (a) the impulse and (b) the average force on the wall? (c) During a time interval of many impacts, what is the magnitude of the average force on the wall?
7. Particle A and particle B are held together with a compressed spring between them. When they are released, the spring pushes them apart and they then fly off in opposite directions, free of the spring. The mass of A is 5.00 times the mass of B, and the energy stored in the spring was 30 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of (a) particle A and (b) particle B?
a. 5 J
b. 25 J
8. In the figure, two long barges are moving in the same direction in still water, one with a speed of 8.1 km/h and the other with a speed of 24 km/h. While they are passing each other, coal is shoveled from the slower to the faster one at a rate of 710 kg/min. How much additional force must be provided by the driving engines of (a) the faster barge and (b) the slower barge if neither is to change speed? Assume that the shoveling is always perfectly sideways and that the frictional forces between the barges and the water do not depend on the mass of the barges.
9. The figure shows a uniform square plate of edge length 6d = 8.0 m from which a square piece of edge length 2d has been removed. What are (a) the x coordinate and (b) the ycoordinate of the center of mass of the remaining piece?
10. A man (weighing 797 N) stands on a long railroad flatcar (weighing 2545 N) as it rolls at 16.3 m/s in the positive direction of an x axis, with negligible friction. Then the man runs along the flatcar in the negative x direction at 4.75 m/s relative to the flatcar. What is the resulting increase in the speed of the flatcar?
1.133 Units: m/s