Physics Problems: Solutions and Explanations
1. Which of the following statements is correct? Functions of the form y = kxn always give a straight line when plotted on logarithmic paper.
2. Note which of the following results is correct, based on the theory of computation error: (0.23)3 = 0.012.
3. In an experiment, a ball of plasticine falls from a height H = 3.00 ± 0.02 m. The gravity is g = 9.81 ± 0.01 ms-2. If errors are given by uncertainties, the velocity of the ball just before impact with the ground is closer to 7.67 ± 0.03 ms-1.
4. In a laboratory experiment that makes an angle with the horizontal, θ = 72.8° ± 0.4°, where the error is clearly specified as uncertainty. The value of cos(θ) is closer to 0.296 ± 0.07.
5. By measuring a piece with a bore, we obtained the following results in mm: 8.47, 8.31, 8.67, 8.52, 8.71, 8.49, 8.71, 8.39. If the error is expressed as the standard deviation of the average, the best value for the measurement is closer to 8.57 ± 0.05.
6. A compass indicates a plane is flying north, and the velocimeter indicates that, with respect to the wind, it flies at a speed of 350 km-1. From land, it is reported that a wind of 90 km-1 blows from east to west. The speed of the plane on the ground is closer to 360 km/h, +14º.
7. When it rains, raindrops form an angle of 30° to the vertical when the train has a speed of 45 km/h, but form an angle of 45° when the train has a speed of 90 km/h. The speed of the drops and their angle with respect to the vertical when the train is stationary are closer to 108 km/h, 9º.
8. In a head-on collision between a mosquito and a truck on a road, which of the following findings related to the impact time is correct? The force that the mosquito experiences equals that experienced by the truck.
9. A car travels on a flat, straight track at 120 km/h. Which of the following statements is correct? The total force that acts on the car is zero.
10. Indicate which of the following statements is correct: It may happen that there exists a non-zero net force on a particle, and its speed does not change.
11. As seen in the figure, a 5.0 kg block and a 4.0 kg block are connected by a 0.6 kg bar. The unions between the blocks and the bar are denoted by A and B. A force F = 250 N is applied to the upper block. The tension at junction B is closer to 104 N.
12. As shown in the figure, a 4.6 m long bar of negligible mass can rotate without friction about an axis perpendicular to the bar that passes through O. A ball of 8.7 kg is fastened to its other end. The bar and the ball are released from rest at point A, describing an oscillatory movement between points A and B. The tension of the bar when the ball passes through point B is closer to 45 N.
13. In the figure, a constant external force F = 170 N is applied to a box of mass 20 kg, which is on a horizontal surface. The force moves the box a distance of 8.0 m in a time interval of 6.0 s, and the speed of the box changes from 1.0 ms-1 to 0.8 ms-1. The coefficient of kinetic friction is closer to 0.0.
14. A small bead can slide without friction along a circular ring of 0.100 m radius that is in a vertical plane. The ring rotates at a constant speed of 4.00 revolutions per second on a vertical diameter. The angle β at which the bead is in vertical equilibrium is closer to 80º.
15. A child is pushed on a swing with a variable horizontal force, F. The mass of the child is m, and the length of the swing chain is R. The child is pushed from the position where the chain is vertical until it forms an angle θ with the vertical. The chain and the swing have negligible mass. The child starts from rest, and there is no friction. Indicate which of the following statements is correct: The work of the total force acting on the child is null.
16. Two sailboats compete on a frictionless horizontal lake. The yachts have masses m and 2m, respectively, but their sails are identical. If the wind exerts the same constant force F on both, and the yachts start from rest and the target is at a distance s. Which of the following statements is correct: Both yachts reach the goal with the same kinetic energy.
17. State which of the following claims is true (see figure): Curve 3 corresponds to a critical oscillator.
18. A conveyor belt carries 2000 kg of sand per minute to a height of 5 meters. The sand is initially at rest and is ejected from the belt at 6 ms-1. The minimum power value to be supplied to the conveyor belt is closer to 2.2 kW.
19. The figure shows two distinct frictionless ramps. The heights y1 and y2 of each ramp are identical. Releasing a block of mass m from the left end of each ramp, indicate which of the following statements is correct: The speed of arrival in both cases is equal.
20. Two blocks of mass 2 kg and 3 kg are connected by a massless rope that passes, without sliding, over a pulley with a moment of inertia of 0.004 kg/m2 and a radius of 5 cm. The coefficient of friction between the surface and the upper block is 0.30. The blocks are released from rest, as shown in the figure. The speed of the upper block after traveling 0.6 m is closer to 1.40 ms-1.
21. Three homogeneous bodies of equal mass and radius are released with velocity v: a ring, a sphere, and a cylinder, as shown in the figure. Let HR, HS, and HC be the heights reached by the bodies on the incline from position 1 to 2, rolling without slipping at all times. Indicate which of the following statements is correct: HS > HC > HR.
22. A steel ball of 49 g is released from rest and falls vertically until it crashes into a steel plate. The collision lasts 0.5 ms. The ball rebounds elastically to its original position. The return flight time of the ball is 7 s. In this situation, the average force exerted on the ball during contact with the plate is closer to 8360 N.
23. A soccer ball of 0.40 kg initially moves horizontally on the floor to the left with a speed of 20 ms-1. Then it is kicked by a player, so it acquires a speed of 30 ms-1 and a direction of 45° upwards and to the right (see figure). Assuming that the kick lasts 0.01 s, the average net force that the footballer exerts on the ball and its direction to the right are closer to 1900 N, 30°.
24. Two sliders, as shown in the figure, collide. The coefficient of restitution is 0.8. Indicate which of the following statements is correct: The kinetic energy after the collision is less than 0.8 times the kinetic energy before the collision.
25. René and Paco stand with a separation of 20.0 m on the surface of a frozen lake with negligible friction. René has a mass of 60.0 kg and Paco 90.0 kg. Halfway between them is a jar of their favorite beverage. The two pull on a massless rope, trying to reach the jar. Indicate which of the following statements is true: When René has moved 5 m toward the pitcher, Paco has moved approximately 3.3 m.
26. A door of 1.00 m width and 15.0 kg mass is hinged on one side so that it can rotate without friction around a vertical axis. The door is not secured. A policeman fires a bullet of 10.0 g with a speed of 400.0 ms-1 at the exact center of the door, in a direction perpendicular to the door, embedding it. Indicate which of the following statements is correct: The angular momentum of the door-bullet system is conserved.
27. In the figure, a ladder of 200 N weight and length L = 10 m leans against a smooth vertical wall without friction. A firefighter, weighing 900 N, climbs a distance x. The coefficient of friction between the ladder and the floor is 0.5. The maximum value of x for which the ladder does not slide is closer to 6.20 m.
28. Indicate which of the following statements is correct: If the amplitude of a simple pendulum increases, the period increases.
29. A connecting rod of 1.80 kg from a motor rotates around a pivot point, as shown in the figure. The center of gravity was found to be 0.20 m from the pivot. When oscillating with small fluctuations, the rod completes 100 oscillations in 120 s. The moment of inertia of the connecting rod about the axis of rotation passing through the pivot is close to 0.13 kg m2.
30. Consider a brick that is totally immersed in water. Its longest dimension is vertical. The water pressure on the brick is greater on the underside.