CHAPTER 7 HOMEWORK
1. (p.171 Ex.10) What is the minimum work needed to push a 950-kg car 310m up along a 9.0° incline? (a) ignore friction. (b) assume the effective coefficient of friction retarding the car is 0.25.
2. (p.172 Ex.21) If A = 7.0i - 8.5j, B= -8.0i + 8.1j + 4.2k, and C = 6.8i - 7.2j, determine (a) A × (B + C); (b) (A + C) × B; (c) (B + A) × C.
3. (p.172 Ex.33) The net force exerted on a particle acts in the positive x direction. Its magnitude increases linearly from zero at x = 0, to 300N at x = 3.0m. It remains constant at 300N from x = 3.0m to x = 7.0m and then decreases linearly to zero at x = 11.0m. Determine the work done to move the particle from x = 0 to x = 11.0m by graphically determining the area under the F versus x graph.
4. (p.173 Ex.37) The force needed to hold a particular spring compressed an amount x from its normal length is given by F = kx + ax3 + bx4. How much work must be done to compress it by an amount X, starting from x = 0?
5. (p.173 Ex. 49) A force of 6.0N is used to accelerate a mass of 1.0kg from rest for a distance of 12m. The force is applied along the direction of travel. The coefficient of kinetic friction is 0.30. What is the work done (a) by the applied force? (b) by friction? (c) What is the kinetic energy at the 12-m mark?
6. (p.173 Ex.54) A 355-kg load is lifted 33.0m vertically by a single cable with an acceleration a = 0.15g. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it starts from rest.
*7. (p.173 Ex.39) A 2500-kg space vehicle, initially at rest, falls vertically from a height of 3000km above the Earth's surface. (a) Determine how much work is done by the force of gravity in bringing the vehicle to the Earth's surface by first constructing an F versus r graph (using Eq. 7-1), where r is the distance from the Earth's center. Then determine the work graphically to an accuracy of 3 percent. (b) Repeat using integration.
*8 (p.174 Ex.57) An elevator cable breaks when a 755-kg elevator is 22.5m above the top of a huge spring (k = 8.00 x 104N/m) at the bottom of the shaft. Calculate (a) the work done by gravity on the elevator before it hits the spring; (b) the speed of the elevator just before striking the spring; (c) the amount the spring compresses (note that here work is done by both the spring and gravity).