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.