You are working for the Highway Department. In mountainous regions, highways sometimes include a runaway truck ramp, and you are asked to help with the design of such a ramp. A runaway truck ramp is often a lane of gravel adjacent to a long downhill section of roadway where trucks with failing brakes may need assistance to stop. Working with your supervisor, you develop a worst-case scenario: a truck with a mass of 4.50 x 104 kg enters a runaway truck lane traveling at 31.1 m/s. Assume that the maximum constant value for safe acceleration of the truck is -5.00 m/s². Any higher magnitude of acceleration increases the likelihood that semi-trailer rigs could jackknife. Your supervisor asks you to advise her on the required length (in m) of a runaway truck lane on a flat section of ground next to the roadway. m

For t 0, an object of mass m experiences no force and moves in the positive x direction with a constant speed vi. Beginning at t = 0, when the object passes position x = 0, it experiences a net resistive force proportional to the square of its speed: Fnet=mkv2i, where k is a constant. The speed of the object after t = 0 is given by v = vi/(1 + kvit). (a) Find the position x of the object as a function of time. (b) Find the objects velocity as a function of position.

In a tug-of-war game on one campus, 15 students pull on a rope at both ends in an effort to displace the central knot to one side or the other. Two students pull with force 196 N each to the light, four students pull with force 98 N each to the left, five students pull with force 62 N each to the left, three students pull with force 150 N each to the right, and one student pulls with force 250 N to the left. Assuming the positive direction to the tight, express the net pull on the knot in terms of the unit vector. How big is the net pull on the knot? In what direction?

Draw a free-body diagram for the burglar, who is shown at rest while sneaking through a chimney in Figure P6.6.

The shower curtain rod in Figure P6.7 is called a tension rod. The rod is not attached to the wall with screws, nails, or glue, but is pressed into the wall instead. Explain why the rod remains at rest, supporting the curtain. Explain why the name is misleading and come up with a better name. FIGURE P6.7

If the vector components of the position of a particle moving in the xy plane as a function of time are x(t)=(2.5ms2)t2i and y(t)=(5.0ms3)t3j, when is the angle between the net force on the particle and the x axis equal to 45?

When a spacecraft collides with a planet, it is not necessary for them to actually touch each other, but when a car collides with a truck, the car and the truck must touch. Explain the difference between these two types of collisions.

(a) A car with a mass of 850 kg is moving to the right with a constant speed of 1.44 m/s. What is the total force on the car? (b) What is the total force on the car if it is moving to the left?

A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal. Which of the following statements must be true about the magnitude of the frictional force that acts on the crate? (a) It is larger than the weight of the crate. (b) It is at least equal to the weight of the crate. (c) It is equal to sn. (d) It is greater than the component of the gravitational force acting down the ramp. (e) It is equal to the component of the gravitational force acting down the ramp.

A car with a mass of 1453 kg is rolling along a flat stretch of road and eventually comes to a stop due to rolling friction. If the car begins with a speed of 10.0 m/s and the car comes to a stop in 6.88 s, what is the coefficient of rolling friction between the tires and the road?