Chipola College- PHY 1053

General Physics- Energy Example Problems

1. Consider the path of a 80 kg particle moving along the track shown below. Note that there is a patch 32 m long which is characterized by a coefficient of friction m_k=0.5. The spring on the left has a spring constant of 13000 N/m and is compressed by 0.2 m when the particle is traveling at a speed of 7 m/s. For this problem, choose the zero of gravitational potential at the dashed line shown in the diagram.

a) What is the mechanical energy of the particle when it comes off of the spring at point A?

a) How fast is the particle traveling when it gets to the dip at point B?

c) Calculate the velocity of the particle when it gets to point C?

d) Find the velocity of the particle when it arrives at point D.

e) As the particle falls off the track at point D, it travels in free fall for 12 seconds. Calculate the mechanical energy after this time.

2. Consider a 1500 kg car sliding along the ground without friction. To get the car started moving from rest, a force is applied in the direction parallel to the street for a distance of 15 m until it is traveling at 18 m/s. Use work and energy considerations to answer the following questions.

a) Use the work-energy theorem to find the force used to accelerate the car.

b) The car slides down a hill to a stretch of road which is 4 m below the original level. Calculate the velocity of the car at this point. (You do not need to know the answer above for this part).

c) The car comes to a hill which climbs to a height of 25 m. It momentarily comes to rest as it runs out of kinetic energy before it gets to the top of the hill. How high above the original level (where it was pushed) does it rise?

d) What is the mechanical energy of the car in part c)?

e) The car slides back down the hill and then travels back up to its original position. What is the velocity of the car when it gets back to the point from where it was pushed?

3. Consider the action of driving a 1500 kg car down the road which slides along the frictionless surface. Answer the following questions for a car which is initially traveling with a speed of 8 m/s.

a) What is the initial mechanical energy of the car?

b) If the car slides down a 15 m hill, calculate the velocity of the car at the bottom of the hill.

c) You see a truck parked in the middle of the road. As you apply your brakes, a force of friction slows the car for a distance of 20 m before you hit the car. Assuming a coefficient of friction between the asphalt road and the rubber tires of 0.37, then find the speed of the car just before it hits the truck.

d) As you hit the truck, the metal of the body can be treated as a spring with a force constant of 420,000 N/m. How big of a dent will you make in the truck? That is, what is the maximum compression of the metal body?

4. An empty 105 kg roller coaster car slides along the track shown in the figure using spring power. The spring on the left is described by a spring constant with K₁=15,000 N/m and is initially compressed by 1.2 m before the car is set in motion. When the spring is released, the car moves on the track until it hits the spring on the right with K₂=12,000 N/m and momentarily comes to rest. Note the 12.5 m patch of friction characterized by a coefficient of friction m_k=0.5.

a) What is the velocity of the car when it gets to point A after reaching the bottom of the hill (just before the patch of friction).

b) What is the maximum compression of the spring on the right.

c) The car bounces off of the spring on the right and goes back in the direction it came from. Find the velocity of the car just before it returns to the loop shown.

d) As a result of non-conservative work, the roller coaster car cannot make it all the way to the top of the hill on the left after it bounces off of the right spring. What is the maximum height the car reaches on the return trip (traveling left toward K₁)?

5. A particle of mass 20 kg slides along the track shown below. The force constants for the springs are given, and the heights are referenced from the starting position of the mass.

a) The spring is initially compressed on the left, and the mass is set into motion. As the mass begins its journey on the track, it achieves a velocity of 2 m/s when the spring is compressed by 0.95 m. Find the kinetic energy of the particle when it finally leaves the spring at position A.

b) What is the velocity of the mass when it gets to the bottom of the hill at position B.

c) Calculate the maximum compression of the spring on the right (position C).

d) After leaving the spring at position C, the mass travels to a position up the hill to position D. What is the velocity of the mass at this point.

e) Thinking back to part a), find the initial compression of the spring which started the particle in motion.

6. A cart with mass 15 kg slides on the ground along the path shown. The surfaces are frictionless except for a patch of friction the cart encounters on the other side of the hill,characterized by a frictional coefficient m_k=0.15 and length 9m.

a) Using the initial position of the block for zero gravitational potential energy, find the mechanical energy of the cart as it reaches the top of the hill?

b) Find the velocity of the cart just after the mass leaves the spring.

c) What is the velocity of the cart as it reaches the top of the hill?

d) Find the velocity of the cart after it goes over the patch of friction on the right.