The force on a particle is described by the function: F(y) = -b+ay+ where a and b are constants and y is measured from the location where the potential energy is defined to be zero. c) Find an expression for the potential energy of the particle as a function of its position (v). Newtons d) If b = 2 Newtons and a 3 what is the potential energy of the particle (in " m4 Joules) when it is at the position y = 0.2 m? =

7. The work done by gravity in lowering a 3.0 [kg] box from an initial height to the ground is 15 [J]. What is the gravitational potential energy at its initial position if the potential energy at the ground is zero? A. zero B. -15.0 [J] C. +15.0 [J] D. +30.0 [J]

Constructed Response 1 Jim is lying on his back on the ground throwing a ball in the air and catching it. There is a balcony 10 meters above his head onto which he is trying to land the ball. On his last throw the ball lands on the balcony. The graph below shows the potential and kinetic energy of the ball from when it left Jim's hand to when it landed on the balcony. ★ Graivational Potential energy A Kinetic energy 200 180 160 140 120 100 80 60 40 20 0. 0. 4 9. 10 Height (m) 8. 2. Energy (J)

d) What is the applied force when the spring is compressed? e) What is the kinetic energy of the toy when it reaches its maximum height?

1. A roller-coaster car with a mass of 1200 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. [Express your answers in kilojoules (kJ).] a. What is the initial potential energy of the car? b. What is the potential energy at point B? c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40 000 J (40 kJ), what is the kinetic energy of the car at point B 2. The time required for one complete cycle of a mass oscillating at the end of a spring is 0.80 s. What is the frequency of oscillation?

1480 kg car accelerates uniformly from a position of rest to a speed of 95 km/h in 6.0 s. a) Calculate the car's acceleration. b) How far did the car travel during this acceleration?  b) How much work was done by the car during this 6.0 s?

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An object with a mass of 15kg slides down an incline with a length of 6.0m at an angle of 28 degrees from horizontal.  The coefficient of friction between the object and incline is 0.25  a) How much work does the gravitational force perform on the object? b) How much work does the frictional force perform on the object?  c) What will its speed be as it reaches the bottom of the incline?

Q 3. Three cars are traveling at 30km/h, 50km/h and 200km/h, respectively. Each speed corresponds to a certain kinetic energy. a)  Note down the expression for the kinetic energy of a moving object with a velocity v. b)  Note down the potential energy for an object lifted up from the ground to height h. c)  Based on a) and b) find an expression for the height as a function of velocity by assuming that the kinetic energy equals the potential energy of the same object. In other words find h(v) from which the object would need to be dropped and calculate the height so it has a speed of 30 km/h, 50 km/h or 200 km/h on impact with the ground. Assume free fall without air resistance d)  Comment on your chances of survival if you are involved in head-on collisions for the three different speeds.

1) Figure 2 illustrates a block having mass M positioned on a ramp having ramp angle 0 above the horizon. The contacting surfaces have a coefficient of kinetic friction, lk. The block is released from rest and it slides down the ramp such that the magnitude of its vertical displacement is H. The speed of the block when it reaches the bottom of the ramp is Vf. Determine expressions {Uk, 0, g, H, M} for the following: a) the work done on the block by friction; b) the work done on the block by the normal force; c) the work done on the block by gravity; and d) the final speed V¢ of the block M Figure 2 H