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ENGR 215 ~ Dynamics Sections 14.1 – 14.3
Conservation of Energy• Energy can neither be created nor
destroyed during a process, it can only change forms.
• ` 1 1 2 2T U T T = Kinetic EnergyU = Work
Work Sign Convention
• Work is positive when the force component is in the same direction as the direction of the force.
1 1 2 2T U T
Energy is a State Function
• We are really concerned about changes in energy from one state to another.
The Work of a Force
dU dF r
Work along a Path
dU dF r
2 2
1 1
r s
1 2r s
U d Fcos ds F r
Constant Force along a straight line
Work of a Weight
Work done by a Spring
Sign for Spring Work
• Spring work is positive if the force on the spring and the displacement are in the same direction.
• Spring work is negative if the force on the spring and the displacement are in opposite directions.
Principle of Work and Energy
1 1 2 2T U T
Lecture Example 1: The 0.5 kg ball of negligible size is fired up the vertical circular track. The plunger keeps the spring compressed 0.08m when s=0. Determine how far the spring must be pulled back and released so that the ball will leave the track at θ = 135˚.
Lecture Example 2: A frictionless car with a mass of 1 kg is hooked to a spring (k=10 N/m) on an incline plane with a slope of 1/5. If the car is pulled back 0.5 m from its initial position and released, how fast is the car moving when it passes through the point where the spring is at rest.
Lecture Example 3: The 20-kg crate is subjected to a force having a constant direction and a magnitude F=100N. When s=15m, the crate is moving at 8 m/s. Determine the speed when s= 25 m. The coefficient of friction is μk = 0.25
What about this problem on an incline?
Lecture Example 4: A 1-kg car attached to a spring was stretched a distance, x, from its rest position, x0, and released. The velocity of the car was measured at x0 and plotted below. Determine the spring constant, k, of the spring.
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