#$&* course PHY 241 10/10/10; 16:38 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `aA force Fnet acting on mass m results in acceleration a, where a = Fnet / m. We are given Fnet and a, so we can solve the equation to find m. Multiplying both sides by m we get a * m = Fnet / m * m so a * m = Fnet. Dividing both sides of this equation by a we have m = Fnet / a = 265 N / (2.30 m/s^2) = 115 (kg m/s^2) / (m/s^2) = 115 kg. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): good enough ------------------------------------------------ self-critique rating #$&*: K ********************************************* Question: `qprin phy and gen phy problem 4.07: force to accelerate 7 g pellet to 125 m/s in .7 m barrel YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: F_net=ma Force = mass * acceleration We have enough info to find the v ave and the distance so we cand find the `dt and then indirectly the acceleration. The v Ave, if acceleration is constant, is (v0+v1)/2 =>125/2 = 62.5 m/s the `dt = `ds/v_ave = .7/62.5 = about .011sec the `dv/`dt= a => 62.5m/s / .011s = a = about 11.2 km/s^s =a 7/1000 kg = mass[m], 11.2 m/s^2 = a => F_net=m[7/1000kg]*a[11160m/s^2]=.007kg*11.2km/s^2 = 78.125 kg*m/s^2 or N or B.c. net force is mass * acceleration we simply multiply the two values given and we have the net force. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The initial velocity of the bullet is zero and the final velocity is 125 m/s. If we assume uniform acceleration (not necessarily the case but not a bad first approximation) the average velocity is (0 + 125 m/s) / 2 = 62.5 m/s and the time required for the trip down the barrel is .7 m / (62.5 m/s) = .011 sec, approx.. Acceleration is therefore rate of velocity change = `dv / `dt = (125 m/s - 0 m/s) / (.011 sec) = 11000 m/s^2, approx.. The force on the bullet is therefore F = m a = .007 kg * 11000 m/s^2 = 77 N approx. ** STUDENT COMMENT: I did my answer a different way and came up with a number just off of this. I calculated 78 and this solution shows an answer of 77, but I am positive that I did my work right. INSTRUCTOR RESPONSE: The results of my numerical calculations are always to be regarded as 'fuzzy'. The calculations are done mentally and there is often no intent to be exact. This at the very least encourages students to do the arithmetic and think about significant figures for themselves. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I did the same as the prior student! Yeah for me Self-critique Rating: ********************************************* Question: `qgen phy 4.08. A fish is being pulled upward. The breaking strength of the line holding the fish is 22 N. An acceleration of 2.5 m/s^2 breaks the line. What can we say about the mass of the fish? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 22<2.5*m => m is < 8.8 kg. If the line can withstand a 2 N force and we neglect the weight of the line and the force of the water ect. Then the F_net=ma so if the force acting on the string is greater than the strings strength the line will break. If we know the speed of the string we can find the min weight of the fish. ST 22 kg*m/s^2 < or= 2.5 m/s^2 *m [kg]= 22/2.5
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Given Solution: ok `aThe fish is being pulled upward by the tension, downward by gravity. The net force on the fish is therefore equal to the tension in the line, minus the force exerted by gravity. In symbols, Fnet = T - M g, where M is the mass of the fish. (We use capital M for the mass of the fish to distinguish the symbol for mass from the symbol m for meter). To accelerate a fish of mass M upward at 2.5 m/s^2 the net force must be Fnet = M a = M * 2.5 m/s^2. Combined with the preceding we have the condition M * 2.5 m/s^2 = T - M g so that to provide this force we require T = M * 2.5 m/s^2 + M g = M * 2.5 m/s^2 + M * 9.8 m/s^2 = M * 12.3 m/s^2. We know that the line breaks, so the tension must exceed the 22 N breaking strength of the line. So T > 22 N. Thus M * 12.3 m/s^2 > 22 N. Solving this inequality for m we get M > 22 N / (12.3 m/s^2) = 22 kg m/s^2 / (12.3 m/s^2) = 1.8 kg. The fish has a mass exceeding 1.8 kg. STUDENT QUESTION I had trouble understanding this question to begin with. I am a little confused on why the net force equals an acceleration of 12.3. INSTRUCTOR RESPONSE F_net = M a = M * 2.5 m/s^2, as expressed in the equation F_net = T - m g so that • M * 2.5 m/s^2 = T - M g. It is the tension, not the net force, that ends up with a factor of 12.3 m/s^2: • T = F_net + M g = M * 2.5 m/s^2 + M * 9.8 m/s^2, which is where the 12.3 m/s^2 comes from. Nothing actually accelerates at 12.3 m/s^2, just as nothing in this system accelerates at 9.8 m/s^2. • 9.8 m/s^2 is the acceleration of gravity so M * 9.8 m/s^2 is the force exerted by gravity on the fish. • M * 2.5 m/s^2 is the net force on the fish. • To not only pull the fish upward against gravity, but to also accelerate it at 2.5 m/s^2, requires a tension force of M * 2.5 m/s^2 in addition to the force required to overcome gravity. Thus the tension force is M * 2.5 m/s^2 + M * 9.8 m/s^2 = M * 12.3 m/s^2. STUDENT QUESTION So the T does not really factor out of the equation it is just known that it is greater thatn or less than the Fnet? INSTRUCTOR RESPONSE • Fnet is M * 2.5 m/s^2. • We know that T = M * 12.3 m/s^2. • We know that since the string breaks T is at least 22 N. So M * 12.3 m/s^2 is at least 22 N, and M must be at least 22 N / 12.3 m/s^2 = 1.8 kg. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):I forgot about gravity – darn. I had no trouble find the mass of the fish in the water see my solution. I do understand what I missed and will try not to forget as gravity is always acting on objects on earth – du. T = m*g+m*2.5; solving we get the the result for sybolis sol T/( a_g+a [relative to 0 gravity]) < or = m so 22 N/[2.5+9.8]m/s^2 = 1.8 kg ------------------------------------------------ self-critique rating #$&*: ********************************************* Question: `quniv phy 4.42 (11th edition 4.38) parachutist 55 kg with parachute, upward 620 N force. What are the weight and acceleration of parachutist? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Weight = m*g=>55kg* 9.8=539 N or kg*m/s^2. F_parachutist down = weight; I choose down to be negative and upward to be positive. F_net = 620N [b.c.it is in the upward /+ direction] -539N[b.c. it is in the – direction] = 81 N[neglecting the mass of the parachute]. Acceleration: a=F_net / mass[of the whole system]= 81N/55kg=1.47m/s^2 ------------------------------------------------ self-critique rating #$&*: ********************************************* Question: `qDescribe the free body diagram you drew. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I drew a circle, the man and parachute then I drew a line rep a vector for the force up[due to the parachute]. Then I drew an arrow down rep the a_g After calculating the F_g and I added a third vector rep the net force of the system. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe weight of the parachutist is 55 kg * 9.8 m/s^2 = 540 N, approx.. So the parachutist experiences a downward force of 540 N and an upward force of 620 N. Choosing upward as the positive direction the forces are -540 N and + 620 N, so the net force is -540 + 620 N = 80 N. Your free body diagram should clearly show these two forces, one acting upward and the other downward. The acceleration of the parachutist is a = Fnet / m = +80 N / (55 kg) = 1.4 m/s^2, approx.. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I think I got it—maybe… remembering gravity exists helps.
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Given Solution: `a** Weight is force exerted by gravity. Net force is Fnet = m * a. The forces acting on the fish are the 50 N upward force exerted by the cable and the downward force m g exerted by gravity. So m a = 50 N - m g, which we solve for m to get m = 50 N / (a + g) = 50 N / (2.45 m/s^2 + 9.8 m/s^2) = 50 N / 12.25 m/s^2 = 4 kg. If the balance reads 30 N then F_net = m a = 30 N - m g = 30 N - 4 kg * 9.8 m/s^2 = -9.2 N so a = -9.2 N / (4 kg) = -2.3 m/s^2; i.e., the elevator is accelerating downward at 2.3 m/s^2. If the cable breaks then the fish and everything else in the elevator will accelerate downward at 9.8 m/s^2. Net force will be -m g; net force is also Fbalance - m g. So -m g = Fbalance - m g and we conclude that the balance exerts no force. So it reads 0. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK – I did not understand the string being cut. But after reading though the soln it made sense—I explained the soln. in the initial soln. A bigger problem is that I knew [due to relative accelerations] that the accelerations were additive. The initial eqtn. I did not know why what goes on what side.
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Given Solution: `a** Think in terms of net force. The net force on the fish must be Fnet = m a = m * 4.5 m/s^2. Net force is tension + weight = T - m g, assuming the upward direction is positive. So T - m g = m a and T = m a + m g. Factoring out m we have T = m ( a + g ) so that m = T / (a + g) = 22 N / (4.5 m/s^2 + 9.8 m/s^2) = 22 N / (14.3 m/s^2) = 1.8 kg, approx.. The same principles apply with the elevator. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Already did! "