course Phy 241
44)A gymnast of mass m climbs a vertical rope attached to the ceiling. You can ignore the weight of the rope. Draw a free-body diagram for the gymnast. Calculate the tension in the rope if the gymnast a)climbs at a constant rate. B) hangs motionless on the rope c) accelerates up the rope:d) slides down the rope with a downward acceleration.
If she climbs at a constant rate, T=m(9.8m/s^2 + 0) or just simply T=mg. If she hangs motionless the tension is the same as the force of her weight which is calculated by multiplying mass by the acceleration of gravity. If she accelerates at a constant rate then T=m(g+a)
48)A uniform cable of weight w hangs vertically downward, supported by an upward force of magnitude w at its top end. What is the tension on the cable a) at its top end b) at its bottom end c) at its middle.
At the top end the tension on the cable is equal to the weight of the entire cable. The tension at the bottom end would be 0, and the tension at the middle would be equal to the weight of half the cable. In this scenario T=mg.
52) A student tries to raise a chain consisting of three identical links. Each link has a mass of 300g. the three-piece chain is connected to a string and then suspended vertically, with the student holding the upper endc of thstraing and pulling upward. Because of the student’s pull, an upward force of 12N is appliesd to the chain by the string. Find acceleration of the chain and the force exerted by the top link on the middle link.
If F=ma, we first need to find the Fnet. The force pulling in a downward direction is the weight of the links. The weight of the links is found by taking .3kg*3*9.8 m/s^2 to yield 8.82 N. Therefore we subtract this from the 12N to get a Fnet of 3.18.
If F=ma we can substitute m as .9 kg and F to be 3.18 to get an acceleration of 3.53 m/s^2.
Now to find the tension between the first chain and the second chain, we use the T=m(g+a), or T=.6(9.8+3.53), or 8N.
All your solutions appear to be correct, and are well expressed. I didn't check your numbers to 3 significant figures, quick mental calculations agree to 1 or 2 places with your results.