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University Physics: Mechanics

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University Physics: Mechanics

Ch5. Newton’s Law of Motion

Lecture 7

Dr.-Ing. Erwin Sitompul

http://zitompul.wordpress.com

A block of mass m1 = 3.7 kg on a frictionless plane inclined at angle θ = 30° is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.3 kg.

What are:

(a) the magnitude of the acceleration of each block,

(b) the direction of the acceleration of the hanging block, and

(c) the tension in the cord?

FN

T

T

a

a

m1gsinθ

m1gcosθ

m2g

m1g

Forces on m1 along the x axis:

Forces on m2 along the y axis:

- What is the meaning of negative sign?

(a) The magnitude of the acceleration of each block

(b) The direction of the acceleration of the hanging block

Assumption: The acceleration points upward

Result: Negative value

Conclusion: The true acceleration points downward

Down

(c) The tension in the cord

A passenger of mass 71.43 kg stands on a platform scale in an elevator cab. We are concerned with the scale reading when the cab is stationary and when it is moving up or down.

(a)Find a general solution for the scale reading, whatever the vertical motion of the cab.

(b) What does the scale read if the cab is stationary or moving upward at a constant 0.5 m/s?

(c)What does the scale read if the cab acceleration upward 3.2 m/s2 and downward at 3.2 m/s2?

(a)Find a general solution for the scale reading, whatever the vertical motion of the cab.

→

- The scale reading is equal to FN, which is the force exerted by the surface of the scale towards the passenger

(b)What does the scale read if the cab is stationary or moving upward at a constant 0.5 m/s?

- In stationary condition or when moving upward with a constant velocity, the acceleration of passenger is zero

(c)What does the scale read if the cab acceleration upward 3.2 m/s2 and downward at 3.2 m/s2?

- If the cab accelerates upward, the magnitude of acceleration is positive

- It the cab accelerates downward, the magnitude of acceleration is negative

What does the scale read if, in case accident happens, the cab falls vertically downward?

The figure below shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). One block has mass m1 = 2.8 kg; the other has mass m2 = 1.3 kg. Determine:

(a) the magnitude of the blocks’ acceleration.

(b) the tension in the cord.

- Atwood Machine

Mass m1

Mass m2

- The acceleration of m1 and m2 have the same magnitude a, oppose in direction.
- We take the acceleration of m1 as negative (downward) and of m2 as positive (upward).

T

a

T

a

m1g

m2g

(a) The magnitude of the blocks’ acceleration

- What happen if m2 > m1?

(b) The tension in the cord

A 2 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 3 m + (4 m/s)t + ct2 – (2 m/s3)t3, with x in meters and t in seconds. The factor c is a constant. At t = 3 s, the force on the particle has a magnitude of 36 N and is in the negative direction of the axis.

What is c?

A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in the figure below. The upper cables make angles of 37° and 53° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100N.

Will the traffic light remain hanging in this situation, or will one of the cables break?

1.What is the net force acting on the ring in the next figure?

New

2.Joe’s Advertising wishes to hang a sign weighing 750.0 N so that cable A, attached to the store makes a 30.0° angle, as shown in the figure. Cable B is horizontal and attached to and adjoining building.

What is the tension in cable B?