Does the kinetic energy of an object depend on the frame of reference in which its motion is measured? Provide an example to prove this point.
Kinetic energy of an object depends on the frame of reference. An example is the kinetic energy of a moving car measured by a person standing outside and another person sitting inside the car.
An object is in motion.
Kinetic energy of a body is its mass times its velocity squared.
The measurement of velocity of an object depends on the frame of reference. A stationary frame will measure one velocity of the object. A moving frame will measure the relative velocity to be the velocity of that object. Thus kinetic energy also depends on the frame of reference. For example, to a person standing beside a road, a moving car has velocity and has kinetic energy, but to a person sitting inside the car, the car is stationary and has no kinetic energy.
A ball of mass is connected by a strong string of length to a pivot and held in place with the string vertical. A wind exerts constant force to the right on the ball as shown in Figure P8.82. The ball is released from rest. The wind makes it swing up to attain maximum height above its starting point before it swings down again. (a) Find as a function of . Evaluate for (b) and (c) . How does behave (d) as approaches zero and (e) as approaches infinity? (f) Now consider the equilibrium height of the ball with the wind blowing. Determine it as a function of . Evaluate the equilibrium height for (g) and (h) going to infinity.
A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A particle slides around the inside edge of the hoop. The particle is given an initial speed of . After one revolution, its speed has dropped to because of friction with the floor. (a) Find the energy transformed from mechanical to internal in the particle hoop floor system as a result of friction in one revolution. (b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.
A block of mass M rests on a table. It is fastened to the lower end of a light, vertical spring. The upper end of the spring is fastened to a block of mass m. The upper block is pushed down by an additional force 3 mg, so the spring compression is . In this configuration, the upper block is released from rest. The spring lifts the lower block off the table. In terms of m, what is the greatest possible value for M?
A toy cannon uses a spring to project a soft rubber ball. The spring is originally compressed by and has a force constant of . When the cannon is fired, the ball moves through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of on the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the ball have maximum speed? (c) What is this maximum speed?
Review: As a prank, someone has balanced a pumpkin at the highest point of a grain silo. The silo is topped with a hemispherical cap that is frictionless when wet. The line from the center of curvature of the cap to the pumpkin makes an angle with the vertical. While you happen to be standing nearby in the middle of a rainy night, a breath of wind makes the pumpkin start sliding downward from rest. It loses contact with the cap when the line from the center of the hemisphere to the pumpkin makes a certain angle with the vertical. What is this angle?
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