EXERCISE 8 Rotational Motion
EXERCISE 8 - Rotational Dynamics, Equilibrium of rigid body
1. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 40.0 N m, what minimum force must be exerted by the mechanic at the end of a 30.0-cm lug wrench to accomplish the task? 133 N
2. A steel band exerts a horizontal force of 80.0 N on a tooth at point B in Figure 1. What is the torque on the root of the tooth about point A? 0.64 Nm
3. Calculate the net torque (magnitude and direction) on the beam in Figure 2 about (a) an axis through O perpendicular to the page and (b) an axis through C perpendicular to the page. + 30 Nm, +36 Nm Figure 1 Figure 2
4. A 500-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 100-N rod as indicated in Figure 3. The left end of the rod is supported by a hinge, and the right end is supported by a thin cable making a 30.0° angle with the vertical. (a) Find the tension T in the cable. (b) Find the horizontal and vertical components of force exerted on the left end of the rod by the hinge. T = 443 N, H = 221 N, V = 217 N
Figure 3 Figure 4
5. A 20.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in Figure 4. A cable at an angle of 30.0° with the beam helps to support the light. Find (a) the tension in the cable and (b) the horizontal and vertical forces exerted on the beam by the pole.
T = 392 N, H = 339 N, V = 0
6. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it as shown in Figure 5. The bonds are 0.100 nm in length, and the angle between the two bonds is 106°. Use the coordinate axes shown, and determine the location of the center of gravity of the molecule. Take the mass of an oxygen atom to be 16 times the mass of a hydrogen atom. x = 6.69 x 10-3 mm, y = 0
7. A constant torque
1. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 40.0 N m, what minimum force must be exerted by the mechanic at the end of a 30.0-cm lug wrench to accomplish the task? 133 N
2. A steel band exerts a horizontal force of 80.0 N on a tooth at point B in Figure 1. What is the torque on the root of the tooth about point A? 0.64 Nm
3. Calculate the net torque (magnitude and direction) on the beam in Figure 2 about (a) an axis through O perpendicular to the page and (b) an axis through C perpendicular to the page. + 30 Nm, +36 Nm Figure 1 Figure 2
4. A 500-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 100-N rod as indicated in Figure 3. The left end of the rod is supported by a hinge, and the right end is supported by a thin cable making a 30.0° angle with the vertical. (a) Find the tension T in the cable. (b) Find the horizontal and vertical components of force exerted on the left end of the rod by the hinge. T = 443 N, H = 221 N, V = 217 N
Figure 3 Figure 4
5. A 20.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in Figure 4. A cable at an angle of 30.0° with the beam helps to support the light. Find (a) the tension in the cable and (b) the horizontal and vertical forces exerted on the beam by the pole.
T = 392 N, H = 339 N, V = 0
6. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it as shown in Figure 5. The bonds are 0.100 nm in length, and the angle between the two bonds is 106°. Use the coordinate axes shown, and determine the location of the center of gravity of the molecule. Take the mass of an oxygen atom to be 16 times the mass of a hydrogen atom. x = 6.69 x 10-3 mm, y = 0
7. A constant torque