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University Physics Volume 1

Challenge Problems

University Physics Volume 1Challenge Problems

Challenge Problems

75.

A horizontal force F→F→ is applied to a uniform sphere in direction exact toward the center of the sphere, as shown below. Find the magnitude of this force so that the sphere remains in static equilibrium. What is the frictional force of the incline on the sphere?

Figure shows a sphere of radius R and mass M that placed at the side of the triangle forming angle Theta with the ground. Force F is applied to the sphere.
76.

When a motor is set on a pivoted mount seen below, its weight can be used to maintain tension in the drive belt. When the motor is not running the tensions T1T1 and T2T2 are equal. The total mass of the platform and the motor is 100.0 kg, and the diameter of the drive belt pulley is 16.0cm.16.0cm. when the motor is off, find: (a) the tension in the belt, and (b) the force at the hinged platform support at point C. Assume that the center of mass of the motor plus platform is at the center of the motor.

Figure shows a motor set on a pivoted mount. The center of the motor is 25 cm above and 30 cm to the right from the support point C. Tension T1 forms a 40 degree angle with the line parallel to the ground. Tension T2 forms a 15 degree angle with the line parallel to the ground.
77.

Two wheels A and B with weights w and 2w, respectively, are connected by a uniform rod with weight w/2, as shown below. The wheels are free to roll on the sloped surfaces. Determine the angle that the rod forms with the horizontal when the system is in equilibrium. Hint: There are five forces acting on the rod, which is two weights of the wheels, two normal reaction forces at points where the wheels make contacts with the wedge, and the weight of the rod.

Figure shows the wheels A and B connected by the rod and located at the opposite side of the right angle triangle. Side at which wheel A is located forms a 60 degree angle with the line parallel to the ground. Side at which wheel B is located forms a 30 degree angle with the line parallel to the ground.
78.

Weights are gradually added to a pan until a wheel of mass M and radius R is pulled over an obstacle of height d, as shown below. What is the minimum mass of the weights plus the pan needed to accomplish this?

Figure shows a pan connected to the wheel by a wire. Wire has mass M and radius R. An obstacle of height D separates wheel from the pan.
79.

In order to lift a shovelful of dirt, a gardener pushes downward on the end of the shovel and pulls upward at distance l2l2 from the end, as shown below. The weight of the shovel is mg→mg→ and acts at the point of application of F→2.F→2. Calculate the magnitudes of the forces F→1F→1 and F→2F→2 as functions of l1,l1, l2,l2, mg, and the weight W of the load. Why do your answers not depend on the angle θθ that the shovel makes with the horizontal?

Figure shows a gardener lifting a shovel full of ground with both hands. Force F1 is applied to the back hand. Force F2 is applied to front hand. Force w is applied to the front of shovel with ground. Distance between the back hand and front of shovel is l1. Distance between the back and front hands is l2. Angle between the shovel and line parallel to the ground is theta.
80.

A uniform rod of length 2R and mass M is attached to a small collar C and rests on a cylindrical surface of radius R, as shown below. If the collar can slide without friction along the vertical guide, find the angle θθ for which the rod is in static equilibrium.

Figure shows a uniform rod of length 2R and mass that M is attached to a small collar C and rests on a cylindrical surface of radius R. Angle between the collar and the line parallel to the ground is theta.
81.

The pole shown below is at a 90.0°90.0° bend in a power line and is therefore subjected to more shear force than poles in straight parts of the line. The tension in each line is 4.00×104N,4.00×104N, at the angles shown. The pole is 15.0 m tall, has an 18.0 cm diameter, and can be considered to have half the strength of hardwood. (a) Calculate the compression of the pole. (b) Find how much it bends and in what direction. (c) Find the tension in a guy wire used to keep the pole straight if it is attached to the top of the pole at an angle of 30.0°30.0° with the vertical. The guy wire is in the opposite direction of the bend.

Figure shows a pole to which two forces T and force Tgw are applied. There is a 90 degree angle between two T forces. There is an 80 degree angle between the plane T forces are applied anf the pole. There is a 30 degree angle between Tgw and the pole.
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