Physics Name ______Fall Semester Practice Free Response Period _____ Part 1 (3) The kinetic energy of the cart immediately before 1. A 0.50 kg cart moves on a straight horizontal track. The it hits the floor graph of velocity vx versus time t for the cart is given below.
2. Several students are riding in bumper cars at an amusement park. The combined mass of car A and its occupants is 250 kg. The combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B and moving to the right at 2.0 m/s when the driver decides to bump into car B, which is at rest.
a. Indicate every time t for which the cart is at rest. a. Car A accelerates at 1.5 m/s2 to a speed of 5.0 m/s and then continues at constant velocity until it strikes car B. Calculate the total time for car A to travel the b. Indicate every time interval for which the |speed| of the 15 m. cart is increasing.
c. Indicate every time interval for which the acceleration is positive. b. After the collision, car B moves to the right at 4.8 m/s. (1) Calculate the speed of car A after the collision.
d. Determine the horizontal position x of the cart at t = 9.0 s if the cart is located at x = 2.0 m at t = 0.
(2) Is the direction of motion of car A after the e. Sketch the acceleration a versus time t graph for the collision to the left, right or is it at rest? Justify motion of the cart from t = 0 to t = 21 s. your answer.
c. Is this a perfectly elastic collision (is energy conserved)? Justify your answer.
f. From t = 25 s until the cart reaches the end of the 3. A spring of unstretched length 0.20 m is placed horizontally track, the cart continues with constant horizontal on a frictionless table. One end of the spring is fixed and velocity. The cart leaves the end of the track and hits the other end is attached to a block of mass M = 8.0 kg. the floor, which is 0.40 m below the track. Neglecting The 8.0 kg block is also attached to a massless string that air resistance, determine each of the following. passes over a small frictionless pulley. A block of mass m (1) The time from when the cart leaves the track until = 4.0 kg hangs from the other end of the string. When this it first hits the floor spring-and-blocks system is in equilibrium, the length of the spring is 0.25 m and the 4.0 kg block is 0.70 m above the floor.
(2) The horizontal distance from the end of the track to the point at which the cart first hits the floor a. Draw free-body diagrams showing and labeling the 5. Blocks 1 and 2 of masses m1 and m2 respectively, are forces on each block when the system is in connected by a light string, as shown above. These blocks equilibrium. are further connected to a block of mass M by another light
string that passes over a pulley of negligible mass and 8 kg 4 kg friction. Blocks 1 and 2 move with a constant velocity v down the inclined plane, which makes an angle with the horizontal. The kinetic frictional force on block 1 is f and that on block 2 is 2f. a. Draw and label all the forces on block m1.
b. Calculate the tension in the string.
c. Calculate the force constant of the spring.
The string is now cut at point P. d. Calculate the time for the 4.0 kg block to hit the floor. Express your answers to each of the following in terms of
m1, m2, g, , and f. b. Determine the coefficient of kinetic friction between e. Calculate the frequency of oscillation of the 8.0 kg the inclined plane and block 1. block.
c. Determine the value of the suspended mass M that f. Calculate the maximum speed of the 8.0 kg block. allows blocks 1 and 2 to move with constant velocity down the plane.
4. A simple pendulum consists of a bob of mass 1.8 kg attached to a string of length 2.3 m. The pendulum is held d. The string between blocks 1 and 2 is now cut. at an angle of 30° from the vertical by a light horizontal Determine the acceleration of block 1 while it is on the string attached to a wall. inclined plane. a. Draw a free-body diagram showing and labeling the forces on the bob in the position shown above.
6. A 800 kg crate is attached to the bed of a 5000 kg truck by Ft a spring (k = 5,000 N/m).
Fw
Fg The truck accelerates to 25 m/s in 10 s along a straight, b. Calculate the tension in the horizontal string. level highway, a. What is the force on the crate during acceleration?
c. The horizontal string is now cut close to the bob, and the pendulum swings down. Calculate the speed of b. What is the coefficient of friction between the crate the bob at its lowest position. and truck bed if the spring stretches 0.08 m during the acceleration?
The truck reaches its cruising speed. c. Does the crate move forward? Part 2 d. Momentum of each photon (in kg•m/s) 7. You are asked to experimentally determine the focal length of a converging lens. a. Sketch the setup used to obtain the object distance do e. Total momentum of both photons (in kg•m/s) and the image distance di. Label the lens, screen, candle, do and di. 9. An experiment is performed using the apparatus. A small disk of mass m1 on a frictionless table is attached to one end of a string. The string passes through a hole in the table and an attached narrow, vertical plastic tube. An b. Complete the last two columns for the following data. object of mass m2 is hung at the other end of the string. A -1 -1 Trial # do (m) 1/do (m ) di (m) 1/di (m ) student holding the tube makes the disk rotate in a circle of 1 0.40 1.10 constant radius r, while another student measures the period T. 2 0.50 0.75 3 0.60 0.60 4 0.80 0.50 5 1.20 0.38
c. Graph 1/di (y-axis) and 1/do (x-axis) and draw a best-fit line through the points. di 3.5 ½ a. Derive the equation T = 2(m1r/m2g) that relates T 3.0 and m2. (hint: Fg-m2 = Fc-m1) 2.5 2.0
1.5 Quantities related to m2 and T can be graphed so that the 1.0 slope of the line can be used to compute an experimental value for g. 0.5 b. What quantities should be graphed to yield a straight 0 line with a slope that could be used to determine g? 0.5 1.0 1.5 2.0 2.5 3.0
do (1) How can you use the graph to determine the focal length of the lens? The procedure is repeated, and the period T is determined for four values of m2, where m1 = 0.012 kg and r = 0.80 m. c. Use the blank rows in the data chart to calculate the (2) Determine the focal length. quantities from part (b)
m2 (kg) 0.020 0.040 0.060 0.080 d. Sketch a 2-ray diagram showing the position of the T (s) 1.40 1.05 0.80 0.75 image from trial 1 above.
d. Plot the quantities calculated above, label the axes, and draw the best-fit line to the data. F F
8. A positron (positively charged electron) and electron are forced to collide at low velocity. As a result they annihilate each other, creating two photons of equal energy moving in opposite directions. Determine the following. a. Energy generated (in J)
b. Energy of each photon (in eV)
c. Wavelength of each photon (in nm) e. Use your graph to calculate the experimental value of g.
1 10. A rod ( = /3) of mass M1 and length d rotates about point P and strikes ball of mass M2 elastically with velocity v1 (figure 1) After the collision the rod is stationary and the ball moves to the right. Answer the questions in terms of M1, M2, v1 and d. Figure 1 Figure 2 P P
d x d M1 v1 v1 M1 M2 M1 a. Using the conservation of angular momentum, determine the velocity v2 of the ball after the elastic collision.
b. Using the conservation of rotational kinetic energy, determine the numerical value of the ratio M1/M2?
A new ball with the same mass, M1, as the rod is placed a distance x from the pivot, P, as shown in figure 2. c. For what value of x will the rod stop moving after hitting the ball elastically? (Hint: repeat the calculations from part (a) and part (b) with the new conditions.)
11. Following a nuclear reaction, a nucleus of aluminum is at rest 27 in an excited state represented by 13Al*, as shown below 27 left. The excited nucleus returns to the ground state 13Al by emitting a gamma ray photon of energy 1.02 MeV, as shown below right. The aluminum nucleus in the ground state has a mass of 4.48 x 10-26 kg.
a. Calculate the wavelength of the emitted photon (in m).
b. Calculate the momentum of the photon (in kg•m/s).
c. Calculate the speed of the recoiling nucleus (in m/s). d. Calculate the kinetic energy of the recoiling nucleus (in J).
12. A thin converging lens L of focal length 10.0 cm is used as a simple magnifier to examine an object O that is placed 6.0 cm from the lens. a. Draw a ray diagram showing at least two incident rays and the position and size of the image formed.
b. Justify whether the image is real or virtual.
c. Calculate the distance of the image from the center of the lens.
d. The object is now moved 3.0 cm to the right, as shown below. How does the height of the new image compare with that of the previous image? Justify your answer.