Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1

Transcription

1 Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building

2 Physics 201 p. 2/1 Work done by a constant force One usually hears: Work (W ) done by a force of magnitude F over a displacement d is given by W = F d.

3 Physics 201 p. 2/1 Work done by a constant force One usually hears: Work (W ) done by a force of magnitude F over a displacement d is given by W = F d. Partially true! For example, the force might be applied at an angle with respect to the direction of motion, or it might vary with position, etc... A more general definition is needed.

4 Physics 201 p. 2/1 Work done by a constant force One usually hears: Work (W ) done by a force of magnitude F over a displacement d is given by W = F d. Partially true! For example, the force might be applied at an angle with respect to the direction of motion, or it might vary with position, etc... A more general definition is needed. The concept of work is very important Energy: capacity to do work.

5 Physics 201 p. 3/1 Work done by a constant force

6 Physics 201 p. 4/1 Work done by a constant force One important point: No displacement No work.

7 Physics 201 p. 4/1 Work done by a constant force One important point: No displacement No work. A block of mass m initially at rest on a frictionless table. Apply a constant force F at an angle θ with respect to the Horizontal. From Newton s second law, F cos θ = ma accelerated motion along the horizontal (F cos θ being the component of the force responsible for that); No motion along the vertical. W = (F cos θ) d

8 Physics 201 p. 5/1 Dot or Scalar Product of 2 vectors A scalar product of two vectors is defined as A B = A B cos θ, with θ being the angle between the two vectors.

9 Physics 201 p. 5/1 Dot or Scalar Product of 2 vectors A scalar product of two vectors is defined as A B = A B cos θ, with θ being the angle between the two vectors. Work: W = F d = F d cos θ

10 Physics 201 p. 5/1 Dot or Scalar Product of 2 vectors A scalar product of two vectors is defined as A B = A B cos θ, with θ being the angle between the two vectors. Work: W = F d = F d cos θ (a) 0 θ < 90 0, W is positive; (b) θ = 90 0, W = 0; (c) θ > 90 0, W is negative.

11 Physics 201 p. 5/1 Dot or Scalar Product of 2 vectors A scalar product of two vectors is defined as A B = A B cos θ, with θ being the angle between the two vectors. Work: W = F d = F d cos θ (a) 0 θ < 90 0, W is positive; (b) θ = 90 0, W = 0; (c) θ > 90 0, W is negative. The unit of work is 1 J = 1N.m

12 Physics 201 p. 6/1 Work done by a constant force

13 Physics 201 p. 7/1 Example A force F is applied horizontally to a 100-kg block which then moves with a constant velocity on a rough surface with a kinetic coefficient of friction µ k = 0.4. What is the work done by the applied force after the block has moved a distance of 3 m? Constant velocity No net force F = f k = µ k N = µ k mg

14 Physics 201 p. 8/1 Example Work done by F after a displacement d: W = F d = µ k mgd = kg 9.81m/s 2 3m = 600J.

15 Physics 201 p. 8/1 Example Work done by F after a displacement d: W = F d = µ k mgd = kg 9.81m/s 2 3m = 600J. Notice that the total work on the body is zero. Why?

16 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion.

17 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion. Acceleration: a = F net m

18 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion. Acceleration: a = F net m v 2 = v ad = v ( F net m )d

19 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion. Acceleration: a = F net m v 2 = v ad = v ( F net m )d W tot = F net d = 1 2 mv2 1 2 mv2 0

20 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion. Acceleration: a = F net m v 2 = v ad = v ( F net m )d W tot = F net d = 1 2 mv2 1 2 mv2 0 Kinetic Energy: K = 1 2 mv2. Unit=J

21 Physics 201 p. 9/1 Work-Energy theorem; Kinetic Energy Take a net force, F net pointing in the direction of motion. Acceleration: a = F net m v 2 = v ad = v ( F net m )d W tot = F net d = 1 2 mv2 1 2 mv2 0 Kinetic Energy: K = 1 2 mv2. Unit=J W tot = K final K initial : Work-Energy Theorem.

22 Physics 201 p. 10/1 Work done by a variable force: Example of a spring The work done by a force in moving an object from x 1 to x 2 is equal to the area under the force curve as a function of position. Example: Work done by a constant force.

23 Physics 201 p. 11/1 Work done by a variable force: Example of a spring When we stretch a spring from its relaxed position at x = 0 to a position x, we provide a force F = kx (the spring provide a restoring force F = kx). Work: W = 1 2 (kx)(x) = 1 2 kx2

24 Physics 201 p. 12/1 Example A block of mass m and speed v collides with a spring and comes to rest after compressing it by a distance x. What is its initial speed in terms of the spring constant k and m? The spring, being compressed, does negative work on the block to slow it down W = 1 2 kx2

25 Physics 201 p. 12/1 Example A block of mass m and speed v collides with a spring and comes to rest after compressing it by a distance x. What is its initial speed in terms of the spring constant k and m? The spring, being compressed, does negative work on the block to slow it down W = 1 2 kx2 K final = 0 and K initial = 1 2 mv2

26 Example A block of mass m and speed v collides with a spring and comes to rest after compressing it by a distance x. What is its initial speed in terms of the spring constant k and m? The spring, being compressed, does negative work on the block to slow it down W = 1 2 kx2 K final = 0 and K initial = 1 2 mv2 Work-energy theorem: W = K final K initial 1 2 kx2 = 1 2 mv2 v = k m x Physics 201 p. 12/1

27 Physics 201 p. 13/1 Work done by a spring

28 Physics 201 p. 14/1 Power Power = rate at which work is done. P = W t

29 Physics 201 p. 14/1 Power Power = rate at which work is done. P = W t For an oject moving with constant velocity under the influence of a constant force: P = W t = F d t = F v