28. A 0.3kg ball has a speed of 15m/s.
(a.)What is its kinetic energy?
K=
K=
(b.)If its speed is doubled, what is its kinetic energy?
K=
30. Two men push a 2500-kg car from rest to a speed v, doing 5000J of work in the process. During this time, the car moves 25m. Neglecting friction between the car and the road, and internal friction of the car,
(a). What ist the final speed, v of the car?
The net work done on the car is equal to the change in kinetic energy, so;
(b).What is the horizontal force exerted on the car?
32. A 15-g bullett is accelerated in a rifle barrel 72 cm long to a speed of 780m/s. Use the work-energy relation to find the average froce that acts on the bullet while it is being accelerated.
The amount of work that is done on the bullet is equal to its chang in Kinetic Energy so,
34. A horizontal force of 150N is used to push a 40-kg box a distance of 6-m on a horizontal surface. If the box moves at constant speed, find
(a). the work done by the 150-N force
(b). the energy lost due to friction
If there is no acceleration in the direction of motion, Newton's third law states that the frictional force and the applied force must be the same, just in opposite directions.
Here we are going to make theta 180 because it is the opposite direction.
(c). the coefficient of kinetic friction between the box and surface
36. A cart loaded with bricks has a total mass of 18kg and is pulled at constant speed by a rope. The rope is inclined at 20deg above the horizontal, and the cart moves a distance of 20-m on a horizontal surface. The coefficient of kinetic friction between the car and the surface is 0.5.
a. What is the tension in the rope?
In this case, the tension in the rope must equal the applied force. Since there is no acceleration in the x direction, the applied force or Tension in the x direction must equal the frictional force plus the x component of the weight.
b. How much work is done on the cart by the rope?
c. What is the energy lost due to friction?
If the object is moving at a constant velocity (no acceleration) the frictional force and the applied force must be equal. So the energy loss is -2864J
38. A block of mass 12kg slides from rest down a frictionless 35deg incline and is stopped by a strong spring with k = 3000N/m. The block slides a total distance d L = 3.0m from the point of rest to the point where it rest against the spring. When the block comes to rest, how far has the spring been compressed?
To do this problem you must first realize that the total Work done in this system is equal to the change in Kinetic energy and that the change in Kinetic energy is zero, since it start at rest and finishes at rest:
Now it is important to notice that there are two forces in this problem that are doing work. The first one is gravity which is a conservative force, and the second is the force of the spring which changes over distance making it a nonconservative force. You should recognize that when you have a nonconservative force you must integrate over the distane that force is applied.
The work done by the gravity in conservative and we do not need to integrate, but since Newton put all that hard work in to the development of integral calculus, we will integrate. (Out of respect for him, and also because integrals are COOL)(HEHE)
We only need to be concerned with the x component of gravity, because it is the only one that does work.
Going back to our original statement that the Total Work done is zero, we can make the statement:
Evaluating the integrals at there limits.
Now rearrange the equation solving for d, because is the distance the spring has compressed.
Now plug in the values that you are given
L = 3m
k = 3000N/m
theta = 35deg
mass = 12kg
g = 9.8
d = .116
A crate of mass 10kg is pulled up an incline with an initial speed of 1.5m/s. The pulling force is 100N parallel to the incline, which makes an angle of 20deg with the horizontal. If the coefficient of kinetic friction is 0.4, and the crate is pulled as distance of 5m,
a. How much work is done by gravity?
b. How much energy is lost because of friction?
c. How much work is done by the 100N force?
d. What is the change in Kinetic energy of the crate?
e. What is the speed of the crate after it has been pulled 5m?