(a) A block of mass 13.6 kg is sliding at an initial velocity of 4.65 m/s along horizontal surface right. The surface has a coefficient of kinetic friction of 0.254. How far will it slide before coming to rest? Calculate the time it takes to come to rest? (b) A motorcycle and a truck are both moving in the same direction in adjacent lanes on a highway. Mass of the truck is 8 times that of the motorcycle. At a particular truck instant, the speed of the motorcycle is four times as motorcycle 4v large as the speed of the truck v. Calculate the ratio of kinetic energies of the motorcycle and truck. Calculate the ratio of momentum of the two bodies.

A 75.0-g arrow, fired at a speed of 110 m/s to the left, impacts a tree, which it penetrates to a depth of 12.5 cm before coming to a stop. Assuming the force of friction exerted by the tree is constant, what are the magnitude and direction of the friction force acting on the arrow?

Show that the acceleration of any object down an incline where friction behaves simply (that Is, where fk=kN ) is a=(sinkcos) . Note that the acceleration Is independent of mass and reduces to the expression found in the previous problem when friction becomes negligibly small (k=0) .

We know from studying friction forces that static friction increases with increasing normal force between the surfaces, which becomes important for vehicles traveling on icy or snowy roads that have coefficients of static friction much smaller than those of dry pavement. In particular, the greater the normal force on the drive wheels (those coupled to the engine), the better the traction. The horizontal position of the center of mass of a typical compact automobile is located 1.1 m toward the rear as measured from the front wheel axle. The wheelbase (distance from the front wheel axle to the rear wheel axle) is 2.7 m. Assume the car is stationary on level ground and has a weight of 12,000 N. Determine the total normal force on the two front tires and on the two rear tires. Which do you suppose are the drive wheels in this case?

An aluminum block of mass m1 = 2.00 kg and a copper block of mass m2 = 6.00 kg are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in Figure P5.46, where = 30.0. (a) When they are released from rest, will they start to move? If they do, determine (b) their acceleration and (c) the tension in the string. If they do not move, determine (d) the sum of the magnitudes of the forces of friction acting on the blocks. Figure P5.46

The x and y coordinates of a 4.00-kg particle moving in the xy plane under the influence of a net force F are given by x = t4 6t and y = 4t2 + 1, with x and y in meters and t in seconds. What is the magnitude of the force F at t = 4.00 s?

In a television commercial, a small, spherical bead of mass 4.00 g is released from rest at t=0in a bottle of liquid shampoo. The terminal speed is observed to be 2.00 cm/s. Find (a) the value of the constant bin the equation v=mgb(1ebt/m), and (b) the value of the resistive force when the bead reaches terminal speed.

Check Your Understanding If atmospheric resistance is neglected find the maximum height for the mortar shell. Is calculus required for this solution?

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?

Three skydivers are plummeting earthward. They are initially holding onto each other, but then push apart. Two skydivers of mass 70 and 80 kg gain horizontal velocities of 1.2 m/s north and 1.4 m/s southeast, respectively. What is the horizontal velocity of the third skydiver, whose mass is 55 kg?