UCSD Physics 10
Chapter 6 Work • Work is done on a system where an applied force is associated with displacement * Force and displacement must both be present. • A force with no displacement does no work • A displacement with no applied force has had no work done Definition of Work
• Work is done only when components of a force are parallel to a displacement.
W = (Fparallel) d Work has no direction.
The work done by a force is a scalar physical quantity, even though FORCE is a vector.
4 The VERTICAL component of the force DOES NOT cause the block to move the right. The energy imparted to the box is > evident by its motion to the right. Therefore ONLY the HORIZONTAL COMPONENT of the force actually transfers energy or DOES WORK. If the Force is applied at an angle…
W = F d cos q definition of work d - the displacement of the point of application of the force θ - is the angle between the force and the displacement vectors Work
W = F d cos q definition of work
Units: N m = Joule [J] = 1(kg m/s2) m= kg m2/s2
[force] [displacement] 7 The VERTICAL component of the force DOES NOT cause the block to move the right. The energy imparted to the box is Work evident by its motion to the right. Therefore ONLY the HORIZONTAL COMPONENT of the force actually transfers energy or DOES WORK.
When the FORCE and DISPLACEMENT are in the SAME DIRECTION you get a POSITIVE WORK VALUE. The ANGLE between the force and displacement is ZERO degrees. What happens when you put this in for the COSINE?
When the FORCE and DISPLACEMENT are in the OPPOSITE direction, yet still on the same axis, you get a NEGATIVE WORK VAL UE . This negative doesn't mean the direction, it means loss of energy. In other words, the block does work on the surface. (Work is not done on the block, but by the block). The ANGLE between the force and displacement in this case is 180 degrees. What happens when you put this in for the COSINE?
When the FORCE and DISPLACEMENT are PERPENDICULAR, you get NO WORK!!! The ANGLE between the force and displacement, in this case, is 90 degrees. What happens when you put this in for the COSINE? Summary
Force in same Direction as motion Force opposes Direction of motion
W = F d cos q
But the sign on work will take care of itself if you’ve assigned the angle correctly. Work Jargon • Whenever a force is exerted on a moving object, we say that work is done by the force or by the agent exerting the force.
• If work is negative, this means work was done by the object on the agent. For example, when a box slides across a rough surface the work done against friction is negative, and we say that the object did work on the surface. Kinetic Energy Kinetic Energy
An object in motion has kinetic energy:
K.E. = ½ mv2 m = mass v = speed (magnitude of velocity) The unit of kinetic energy is Joules (J). Kinetic energy is a scalar (magnitude only) Kinetic energy is non-negative (zero or positive) Work is change in K.E. W = F x W = m a x 2 2 and recall that vf = vi + 2 a x 2 2 rearranging… a x = (vf - vi ) / 2
So W = m a x 2 2 = m (vf - vi ) / 2
2 2 W = ½ m vf – ½ m vi Where ½ m v2 is Kinetic Energy Work and Kinetic Energy another look at the equation we just derived: 2 2 W = ½ m vf – ½ m vi
means…
W = KEf – KEi W = DKE
How do we give an object kinetic energy? By doing work! Which requires more work: increasing the speed of an object from 0 m/s to 5 m/s or from 5 m/s to 10 m/s?
Why is this so? Potential Energy
• Kinetic energy is energy of motion
• Potential energy is the stored energy of position possessed by an object. – the object has potential to move because of its position relative to some other location – two types of PE we will discuss are gravitational PE and elastic PE Potential Energy PE (U)
An object can store energy as the result of its position.
17 Gravitational Potential Energy When we do work on an object, we give it energy. Sometimes that energy is in the form of potential energy. Therefore, W = FDx = DPE h
For gravity (near Earth’s surface), where F = mg,
D PE = mgh 18 Elastic Energy Compression and Extension of a Spring
• It takes force to press a • It takes force to extend spring together. a spring.
• More compression • More extension requires requires stronger force. stronger force. Spring Constant
• The distance a spring moves is proportional to the force applied. F µ x
• The ratio of the force to the F distance is the spring constant (k). x k = F / x HOOKE'S LAW The restoring force of an ideal spring is given by F = -k x
where k is the spring constant and x is the displacement of the spring from its unstrained length. The minus sign indicates that the restoring force always points in a direction opposite to the displacement of the spring. Spring Scales Hooke’s Law says Fs = -kDx Fs = -k(-y) • One common use for a spring Fs = ky is to measure weight.
• The displacement of the spring measures the mass.
Fg = mg Force and Distance
• The force applied to a spring increases as the distance increases.
• The product within a small step is the area of a rectangle (kx) Dx.
• The total equals the area between the curve and the x axis. Work on a Spring
• For the spring force, the force makes a straight line.
• The area under the line is the area of a triangle. 1 W = F x s 2 s 1 W = (kx)x s 2 1 W = kx 2 s 2 Elastic Potential Energy
2 • PEelastic = ½ k x
where k is a “spring constant” * and x is the distance compressed or stretched
*k is small for flexible springs, and large for stiff springs. Using Hooke’s Law to find k F = ky • Sometimes you may have to s use Hooke’s law to find k , before solving a problem involving elastic potential energy (PE = ½ kx2)
Fg = mg Work- Energy Theorem: Energy is Conserved
Physics 1050 -- Fall 2005 28 Conservation of Energy
Mechanical Energy is often defined as the ability to do work.
Mechanical Energy exists as potential energy or kinetic energy or both.