Physics Assignment 10 Problems 2015

Question 1

Any vector (displacement, velocity, acceleration or force) can be composed into two rectangle components along two axis perpendicular to each other. Along a same axis, algebraic sum can be used to get the vector sum of all vectors/components along the axis. In this way, the vector sums of the two rectangle components can be obtained. The two rectangle components can then compose into a vector, in return, using trigonometric equations, to know the magnitude and angle of the composed vector.

Three forces (G, R and F) are acting on an object, as shown in the figure. The magnitudes for G, R and F are 10, 15 and 20, respectively. (a) What are their horizontal and vertical components, respectively? (b) How many Newtons are the vector sums of the components along x and y axis, respectively? (c) What are the magnitude and angle of the net force on the object? (d) If the mass of the object is 10 kg, what are the magnitude and angle of the acceleration on the object? (e) What are the horizontal and vertical components of the acceleration?

Question 2

Velocity and acceleration of an object can help to predict its position at any time. In a one-dimensional motion, displacement, velocity and acceleration are along an axis. Change of velocity caused by acceleration plus initial velocity (algebraic sum) can get the velocity at any time. Displacement due to the varying velocity can be predicted accordingly. Now a ball is thrown, from the ground, vertically upwards with an initial velocity of 20 m/s. The gravitational acceleration is 9.8 m/s² downwards. (a) What is the velocity at 2 s after the ball is thrown? (b) How many meters above the ground at that moment? (c) When will the ball stop rising? (d) Where is it at that time? (e) When will the ball drop back to the ground?

In a two-dimensional motion, the motion (displacement, velocity and acceleration) can be decomposed into two perpendicular motions (e.g. horizontal and vertical motions). The two motions are independent to each other. It means that, e.g., displacement along horizontal direction can be calculated based ONLY on horizontal velocity and acceleration or their horizontal components, and don’t need to consider the displacement, velocity and acceleration along vertical direction. Similarly, instantaneous horizontal velocity at any time can be predicted ONLY by horizontal acceleration and initial horizontal velocity as well. The ONLY link between the horizontal and vertical motions is the shared time. It means that at any moment when the object undergoes a certain horizontal motions to achieve a certain horizontal displacement/velocity after a certain period from initial time with the horizontal acceleration and initial velocity, the object at the same time undergoes a certain vertical motion to achieve a certain vertical displacement/velocity using the SAME DURATION, with the vertical acceleration and initial vertical velocity. Now the direction of the initial velocity of the ball in last question is not vertical but upward with an angle of 45^o with horizontal direction. (a) Where is the ball (its horizontal and vertical coordinate at that moment) at 2 s after it is thrown? (b) What are the horizontal and vertical velocities at that moment? (c) When will the ball stop rising? (d) Where is it at that time? (e) When will the ball drop back to the ground? (f) How far away will it be at the moment, from the place where it is thrown?

Question 3

Five adults enter an electric lift. After a man presses the upward button, the lift begins to move up with an acceleration of 1 m/s². The weight of the 5 adults is 350 kg, and that of the lift body is 100 kg. If the lift is hoisted by only a wire rope and all frictions are negligible. Ask (a) after the adults get into the lift and before the upward button is pressed, what is the tension of the wire rope, and (b) when the lift is moving up, what is the tension of the rope.

Question 4

A ball hung at the bottom end of a string with a length of 0.5 m undergoes a horizontal circular motion with a radius of 0.2 m. (a) What force acts as the centripetal force for the circular motion of the ball? (b) What is the magnitude of centripetal acceleration? (c) What is its angular velocity? (d) How many minutes for the ball to finish 100 revolution? Note: the friction can be neglected in the present question.

Question 5

A 2 kg box is placed on an inclined surface (with an angle of 10^o) in a running vehicle. The static and kinetic coefficients of friction between the box and the slope surface are 0.6 and 0.3, respectively. What is the range of the vehicle’s acceleration to avoid the box’s movement relative to the inclined surface? Assume: The vehicle runs in a straight line. (Tips: the acceleration can be leftward or rightward.)

Question 6

The long arm of a crane tower is 19 m long, while its short arm is 8 m. The weight of former is 100 kg while the latter is 40 kg. Its designed maximum hanging load is 50 kg. The fixed counterweight (G3) at the end of the short arm is of 100 kg. What should the weight be for the movable counterweight (G2), which can move from the supporting column to the end of the short arm? Assume that G2 is very short, and the masses of long and short arms are uniform, respectively.

Question 7

A swimming pool has dimensions 50.0 m × 20.0 m and a flat bottom. When the pool is filled to a depth of 1.9 m with fresh water, what is the force exerted by the water on (a) the bottom? (b) On each end? (c) On each side?

Question 8

A huge water tank, filled with water, develops a small hole in its side at a point 10 m below the water level. The pool’s top is open. The rate of flow from the leak is found to be 4.6 l/min. Determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole. (Tips: friction can be neglected. Bernouilli equation should be used.)

Question 9

The food calorie, equal to 4186 J, is a measure of how much energy is released when food is metabolized by the body. A certain brand of fruit-and-cereal bar contains 10 food calories per bar. (a) If a 65-kg hiker eats one of these bars, how high a mountain must he climb to “work off” the calories, assuming that all the food energy goes only into increasing gravitational potential energy? (b) If, as is typical, only 20% of the food calories go into mechanical energy, what would be the answer to part (a)? (Note: In this and all other problems, we are assuming that 100% of the food calories that are eaten are absorbed and used by the body. This is actually not true. A person’s “metabolic ef?ciency” is the percentage of calories eaten that are actually used; the rest are eliminated by the body. Metabolic ef?ciency varies considerably from person to person.)

Question 10

(I) A 1.50 g package is released on a 60^o inclined slope, 6.0 m from a long spring with rigidity coefficient 2.10 × 10² N/m that is attached at the bottom of the slope. The friction between the package and the slope surface and the mass of the spring are negligible. What is the maximum compression of the spring? (Tips: make use of conservation of mechanical energy)

(II) If the coef?cients of friction between the package and incline are µ_s=0.4 and µ_k=0.25. (a) What is the maximum compression of the spring? (b) The package rebounds up the incline. How close does it get to its original position? (Tips: work done by non-conservative forces equals to variation of mechanical energy)