1 Ch 7 Homework Name: Homework problems are from the Serway & Vuille 10 th edition. Follow the instructions and show your work clearly. 1. (Problem 7) A machine part rotates at an angular speed of 0.06 rad/s; its speed is then increased to 2.2 rad/s at and angular acceleration of 0.70 rad/s 2. (a) Label physical quantities in this problem using letters you choose. (b) Find the angle through which the part rotates before reaching this final speed.(first, write down an equation you will use and substitute numerical values in the equation) (c) In general, if both the initial and final angular speeds are doubled at the same angular acceleration, by what factor is the angular displacement changed? Why? (Hint: Look at the form of equation 7.9)
2 2.(Problem 12) A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 rad/s 2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes and angle of 57.3 with the positive x-axis at this time. At t= 2.30 s, find (a) the angular speed of the wheel, (b) the linear velocity and tangential acceleration of P, and (c) the position of P(in degree, with respect to the positive x-axis) (a) Complete the table below. Physical quantity Variable Numerical value Radius of the disk r Angular acceleration α Initial angle θ 0 Initial angular speed ω 0 Final angle θ f? Final angular speed ω f? Linear velocity v? Tangential acceleration a? (b) Using variables defined above, find the angular speed of the wheel and substitute numbers to the equation.
3 (c) Find the liner velocity and tangential acceleration of P in terms of the variables above and substitute numbers to the variable. (d) Find the position of P. 3. (Problem 16) It has been suggested that rotating cylinders about 10 miles long and 5.0 miles in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth? (a) Draw a diagram and label physical quantities using variables you choose.
4 (b) Convert distances from mile to m. (c) Find the angular acceleration in terms of radius and angular speed. (d) Find the angular speed of the colony when the centripetal acceleration at its surface is g =9.8 m/s 2.
5 4. (Problem 19) One end of a cord is fixed and a small kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.00 m as shown in the figure below. When θ = 20.0, the speed of the object is 8.00 m/s. (a) Draw forces on the diagram above and label physical quantities using letters you choose.
6 (b) Write down the tangential and radial components of forces. Radial direction(y-direction) Tension in radial direction Weight in radial direction F nety Tangential direction(x-direction) Tension in tangential direction Weight in tangential direction. F netx (c) Find the tension in the spring. (d) Find the tangential and radial components of acceleration.
7 (e) Find the magnitude and direction of the total acceleration. (f) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? (g) Explain your answer to part (f)
8 5. (Problem 27) An air puck of mass m 1 = 0.25 kg is tied to a string and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m 2 = 1.0 kg is tied to it. (See the figure below.) The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) Label all physical quantities using variables you choose. (b) Draw a free-body diagram of the puck.
9 (c) What is the tension in the string? (d) What is the horizontal force acting on the puck? (e) What is the speed of the puck?
10 6. (Problem 34) A satellite has a mass of 100 kg and is located at above the surface of Earth. (a) Draw a diagram and label all physical quantities in this problem using letters you choose. (b) What is the potential energy associated with the satellite at this location? (c) What is the magnitude of the gravitational force on the satellite?
11 7. (Problem 37) Objects with masses of 200 kg and 500 kg are separated by m (a) Find the net force exerted by these objects on a 50.0 kg object placed midway between them. (b) At what position (other than infinitely remote ones) can the 50.0-kg object be placed so as to experience a net force of zero? a. Find the net force exerted by the 200 kg and 500 kg objects on the 50.0-kg object placed distance d m away from the 200-kg object and (0.400 d) m away from the 500-kg object.(see the diagram below)
12 b. Find the distance d at which the net force on the 50.0-kg object is zero. 8. (Problem 41) A satellite is in a circular orbit around the Earth at an altitude of m. (a) Find the period of the orbit.
13 (b) Find the speed of the satellite (c) Find the acceleration of the satellite.(hint: Modify Equation 7.23 so it is suitable for objects orbiting the Earth than the Sun
14 9. (Problem 71) A 4.00-kg object is attached to a vertical rod by two strings as shown in Figure below. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) the upper string and (b) lower string. (a) Draw a free body diagram and define a coordinate system. Then, label all physical quantities using letters you choose.
15 (b) Write down horizontal and vertical components of the forces. Variable x-direction Value in terms of other variables Variable y-direction Value in terms of other variables F netx F nety (c) Find the tension in the upper string. (d) Find the tension in the lower string.