for part a i got 4.78 , Problem 4: A block of massm=D15kg is attached to a spring with spring constant k= 790 N/m. It is initially at rest on an inclined plane that is at an angle of 0= 24 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is 4 0.14.In the initial position, where the spring is compressed by a distance of d 0.11 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero. M Ctheespertta.co 50% Part (a) What is the block's initial mechanical energy, Eo in J? &50% Part (b) If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion. Grade Summary Deductions L=

A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at 20 . (a) What is the acceleration of the piano up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest?

Try the following experiment away from traffic: where you can do it Safely. With the car VOU are driving moving slowly on a Straight, level road, shift the transmission into neutral and let the car coast. At the moment the car comes to a complete slop, step hard on the ln.ike and notice what you feel. Now repeal I he same experiment on a fairly gentle, uphill slope. Explain the difference in what a pet son tiding in the car feels in the two cases. (Brian Popp suggested the idea for this question.)

Check Your Understanding Suppose that Balto in Example 2.10 leaves the game to attend to more important matter, but Astro Clifford and Dug continue playing. Astro and Clifford’s pull on the toy does not change, but Dug rims around and bites on the toy in a different place. With how big a force and in what direction must Dug pull on the toy now to balance out the combined pulls from Clifford and Astro? Illustrate this situation by drawing a vector diagram indicating all forces involved.

A race car travels 825 km around a circular sprint track of radius 1.313 km. How many times did it go around the track?

Which of the following is a vector: a person's height, the altitude on Mt. Everest, the age of the Earth, the boiling point of water, the cost of this book, the Earth's population, the acceleration of gravity?

A stubborn dog is being walked on a leash by its owner. At one point, the dog encounters an interesting scent at some spot on the ground and wants to explore It in detail, but the owner gets impatient and pulls on the leash with force along the leash. (a) What is the magnitude of the pulling force? (b) What angle does the leash make with the vertical?

between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .

A car is traveling at a speed of 33 m/s. (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

(a) If AF=BF , can we conclude A=B ? (b) If AF=BF , can we conclude A=B ? (c) If FA=BF , can we conclude A=B ? Why or why not?