Practice problems

1. A 12 kg penguin is sliding at 5.8 m/s over frictionless snow and encounters a dip in the snow. She starts at a height 4.5 m above the bottom of the dip. How fast is she moving when she reaches a height of 6.1 m at the other side?

2. A block of mass m starts from rest and slides a distance d1 down a stationary ramp of angle θ and then along the floor a distance d2 before coming to a stop. Assume there is friction between the block and ramp, and between the block and floor, both characterized by the same coefficient of kinetic friction.

 

What is the coefficient of kinetic friction?

 

Consider the case where d1 = 7.8 m, d2 = 7.2 m and θ = 14 degrees.

3. A 12 kg penguin starts from rest on a 45 m high slope with angle 32 degrees. She slides down the frictionless slope against a horizontal 68 N headwind.

 

  A. What is the work done on the penguin by the wind?

 

  B. How fast is the penguin moving at the bottom of the slope?

4. A 12 kg penguin is on a slide at a water park. She starts from rest at a height of 16 m and exits horizontally at a height of 4.3 m, entering the water at a distance of 3.8 m as shown. How much energy was lost to friction between the penguin and the slide? 5. A particle undergoes a one-dimensional conservative force given by F = (2.6 N/m2)x2 - (1.4N/m3)x3. Find the change in potential energy of the particle from x = 2.2 m to x = 3.1 m. 6. A rock of mass M is dropped from rest from a height h above the top surface of a spring scale, compressing the spring by a distance Dy at its lowest point. What is the spring constant of the spring? Consider the case where M = 5.6 kg, h = 3.6 m and Dy = 0.27 m. Use g = 9.8 m/s2.

 

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