A bucket of water with total mass 24.0 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.35 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that the cylinder turns on frictionless bearings, and that g = 9.8 m/s2.)
a. 1 600 N b. 3.4 N
c. 34 N d. 670 N
e. 4.1 N
[Ques. 2] A bucket filled with water has a mass of 20.0 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.80 m/s2)
a. 19.6 Nm b. 9.8 Nm
c. 1.00 Nm d. 400 Nm
e. 196 Nm
[Ques. 3] Two children seat themselves on a seesaw. The one on the left has a weight of 300 N while the one on the right weighs 200 N. The fulcrum is at the midpoint of the seesaw. If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the left? (Take ccw as positive.)
a. 300 Nm b. 300 Nm
c. 450 Nm d. 450 Nm
e. 150 Nm
[Ques. 4] A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark. What is the weight of the meterstick?
a. w b. 1.0w
c. w/1.0 d. 0.70w
e. 0.90w
[Ques. 5] A 3.00-m rod is pivoted about its left end. A force of 7.80 N is applied perpendicular to the rod at a distance of 1.60 m from the pivot causing a ccw torque, and a force of 2.60 N is applied at the end of the rod 3.00 m from the pivot. The 2.60-N force is at an angle of 30.0o to the rod and causes a cw torque. What is the net torque about the pivot? (Take ccw as positive.)
a. 16.4 Nm b. 8.58 Nm
c. 8.58 Nm d. 16.4 Nm
e. 4.68 Nm
[Ques. 6] A bank vault is opened by applying a force of 140 N perpendicular to the plane of the door, 1.20 m from the hinges. Find the torque due to this force about an axis through the hinges.
a. 117 Nm b. 308 Nm
c. 140 Nm d. 168 Nm
e. 154 Nm
[Ques. 7] A machinist needs to punch a 5.0-cm-radius hole in a steel plate which is 0.45 cm thick. If the ultimate shear strength of steel is 2.50 108 Pa, what is the force required to accomplish this task?
a. 8.8E+5 N
b. 3.5E+5 N
c. 5.6E+6 N
d. 1.1E+8 N
[Ques. 8] What is the minimum diameter of a steel wire if it is to support a mass of 80 kg. The elastic limit of steel is 5.0 108 Pa.
a. 1.4 mm
b. 2.0 mm
c. 1.0 mm
d. 2.0 mm
[Ques. 9] How large a force is necessary to stretch a 1.1-mm-diameter steel wire (Y = 2.0 1011 N/m2) by 2.0?
a. 3.8E+6 N
b. 3.8E+3 N
c. 3.8E+6 N
d. 7.6E+7 N
e. 3.8E+3 N
[Ques. 10] A tire stops a car by use of friction. What modulus should we use to calculate the stress and strain on the tire?
a. Young's modulus
b. compression modulus
c. shear modulus
d. bulk modulus
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