PHYSICS 105 Assignment #7 Due by 10 pm October 27, 2009

NAME: ______

DISCUSSION SECTION: [ ] D7 – W 9 am [ ] D8 – W 10 am [ ] HS – W 10 am

[ ] D9 – W 11 am [ ] F 1 – W 1 pm [ ] F2 – W 2 pm [ ] F3 – W 3 pm

[ ] F4 – W 4 pm [ ] F5 – W 7 pm [ ] D1 – F 9 am [ ] D2 – F 10 am

[ ] D3 – F 11 am [ ] D4 – F 12 pm [ ] D5 – F 1 pm (Asma) [ ] D6 – F 1 pm (John)

PLEASE CHECK OFF YOUR DISCUSSION SECTION ABOVE!

INSTRUCTIONS:

1. Please include appropriate units with all numerical answers.

2. Please show all steps in your solutions! If you need more space for calculations, use the back of the page preceding the question. For example, calculations for problem 3 should be done on the back of the page containing question 2. You must show correct work to receive full credit. Support your answers with brief written explanations and/or arguments based on equations.

3. Indicate clearly which part of your solution is the final answer.

4. Try answering these problems, as much as possible, without a calculator and using only the equation sheet to help you. This will help you prepare for the test.

5. Grading scheme for each problem: each part of each problem is worth 2 points. You get 0 if your answer is wrong or mostly wrong, 2 if your answer is correct, and 1 if your answer is mostly correct.

Please do your draft work of the assignment elsewhere, and copy your work over neatly when you hand in the assignment. The graders will deduct points for work that is difficult to follow.

Angle (θ) sin(θ) cos(θ) Problem 1: ____

1 Problem 2: ____3 30˚ 2 Problem 3: 2____ s i n  t a n   2 Problem 4: ____2 45˚c o s  2 Problem 5: 2____ 3 1 60˚ TOTAL: _____ 2 2  PROBLEM 1 – 10 points

The picture above shows the x-axis and a ball of mass m placed at x = 3 (let’s call it the first ball).

(a) [2 points] Where on the axis should we place a second ball, with mass 2m, so the center of mass of the system is located at x = 7?

(b) [2 points] If we keep the balls at these locations, but we can change the mass of the second ball from 0 to infinity, what range do we get for the location of the center of mass of the two-ball system?

(c) [2 points] Negative mass does not exist in nature, but we can use our imagination to find out what would happen if it did. Let’s say we have a third ball which has negative mass m3 = -m. Where should we place it so the center of mass of the system is located at the position of the second ball?

(d) [2 points] Now let’s use a regular ball with a positive mass. Where should we place the third ball, which has the same mass as the first ball, so the center of mass of the system is located at the position of the second ball? (e) [2 points]

The picture above shows the first ball only, but add the second ball to the picture at the location you found in part (a).

Now we need to add a third ball of unknown mass in such a way that the center of mass of the system is located at the point (x = 5, y = 7).

If we know that the third ball is placed somewhere along the dashed line, find its exact location and its mass. PROBLEM 2 – 10 points (1 point for every answer)

A cart that can move along a straight track (aligned with our x axis) has a mass of 8.00 kg and, starting from an initial position of x = +20.0 m, is given an initial velocity of 4.00 m/s in the positive x-direction. The cart is subjected to a net force that is either in the positive or negative x direction, depending on the position of the cart, as shown in the graph. Note that this graph is very similar to the one in Assignment 6, but the force here is plotted as a function of position, rather than time.

[6 points] (a) Complete the table below, to show the cart's kinetic energy and speed at the indicated positions.

Position Kinetic energy Speed x = +20.0 m

x = +10.0 m

x = +5.00 m

(b) What is the farthest the cart gets from x = 0 before it reverses direction for the first time?

(c) What is the change in momentum experienced by the cart as it moves from its initial position, at x = +20.0 m, to the position where it reverses direction for the first time?

(d) How long does the cart take to move from x = +20.0 m to the position where it reverses direction for the first time?

(e) What is the closest the cart gets to x = 0 as it moves back and forth on the track?

PROBLEM 3 – 10 points

30

An object at position A has kinetic energy = 36 J and potential energy  0 J. It slides a distance of 6 m upward along the 30 frictionless incline, before turning around at B. It then slides to a halt at C which is 6 m along the slope below A. The surface below A, between A and C, is rough, rather than frictionless.

(i) What is the potential energy of the object at its highest point (B)? ______

(ii) What is the weight W of the object? ______

(iii) When the object passes through point A on its way down the slope, what is its kinetic energy? ______

(iv) What is the change in the object’s mechanical energy during the entire process, starting at the initial point A and continuing until the final point C? ______

(v) How much work is done on the object by non-conservative forces during the entire process? ______PROBLEM 4 – 8 points

(a) A 20 gram pine cone falls 1.25 m to the ground, where it lands with a speed of 4.0 m/s. Use g = 10 m/s2.

(i) With what speed would the pine cone have landed if there had been no air resistance?

(ii) How much work did air resistance do on the pine cone during its fall? Is your answer positive, negative, or zero? Explain.

(b) The human brain consumes about 20 W of power under normal conditions, though more power may be required during exams.

(i) How long can one Snickers bar power the normally functioning brain? One Snickers bar has about 300 Cal, and 1 Cal is actually equal to 1000 calories. The conversion factor is: 1 Cal = 1000 cal = 1 kcal = 4186 J, although you can use a conversion factor of 1 Cal = 4000 J for this question to practice calculating without a calculator.

(ii) At what speed must you lift a 2.0 kg container of water (a 2-liter bottle) if the power output of your arm is to be 20 W? PROBLEM 5 – 10 points

As shown in the figure, two frictionless ramps are joined by a rough horizontal section that is 4.0 m long. A block is placed at a height of 124 cm up the ramp on the left and released from rest, reaching a maximum height of 108 cm on the ramp on the right before sliding back down again.

[2 points] (a) How far up the ramp on the left does the block get in its subsequent motion?

[2 points] (b) What is the coefficient of kinetic friction between the block and the rough surface?

[2 points] (c) How many times will the block pass completely across the 4.0 m wide rough section? (We’re looking for an integer here)

[2 points] (d) At what location does the block eventually come to a permanent stop?

[2 points] (e) Going back to the very first time the block passes across the rough section, what is the speed of the block when it passes the middle of that rough section the first time across? Use g = 10 m/s2.