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Chapter 9: Q10 P (page 377)

A meter stick whose mass is 300glies on ice (Figure 9.49). You pull at one end of the meter stick, at right to the stick, with a force of 6N. The ensuing motion of the meter stick is quite complicated, but what are the initial magnitude and direction of the rate of change of the momentum of the stick, /dtdpsys, when you first apply the force? What is the magnitude of the initial acceleration of the center of the stick?

Short Answer

Expert verified

The initial magnitude and direction of the rate of change of the momentum of the stick,/dtdpsys is 6N

The magnitude of the initial acceleration of the center of the stick is 20m/s2

Step by step solution

01

Identification of given data

  • The mass of a stick is 300鈥�g(0.3kg)
  • The length of a stick is1m
  • The force applied on a stick is6N
02

Definition of the rate of change of the momentum

According to Newton鈥檚 second law, the rate of change of momentum is equated to the applied force.

03

Calculation of the initial magnitude and direction of the rate of change of the momentum of the stick,

We know that,

The rate of change of momentum is

dpsysdt=F

Where F=6N

dpsysdt=6N

Hence, the initial magnitude of the rate of change of the momentum of the stick, /dtdpsys is 6N

The initial magnitude of the rate of change of the momentum of the stick, is positive (towards the right side).

04

Calculation of the magnitude of the initial acceleration

The force,

F=maa=Fm=6kg路m/s20.3kg=60.3路1kg路m/s21kg=60.3路1m/s2=20m/s2

Hence, the magnitude of the initial acceleration is 20m/s2

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Most popular questions from this chapter

String is wrapped around an object of mass 1.5kg and moment of inertia 0.0015kg-m2(the density of the object is not uniform). With your hand you pull the string straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (Figure 9.62). This is like a yo-yo; nothing but the vertical string touches the object. When your hand is a height y0=0.25mabove the floor, the object has an angular speed 蝇0=12rad/s. When your hand has risen to a height y=0.35m above the floor, what is the angular speed of the object? Your answer must be numeric and not contain the symbol F.

You hang by your hands from a tree limb that is a heightabove the ground, with your center of mass a heightabove the ground and your feet a heightabove the ground, as shown in Figure 9.56. You then let yourself fall. You absorb the shock by bending your knees, ending up momentarily at rest in a crouched position with your center of mass a heightabove the ground. Your mass is M. You will need to draw labeled physics diagrams for the various stages in the process.

(a) What is the net internal energy change 鈭�Eintin your body (chemical plus thermal)? (b) What is your speed vat the instant your feet first touch the ground? (c) What is the approximate average force Fexerted by the ground on your feet when your knees are bending? (d) How much work is done by this force,F?

String is wrapped around an object of mass M and moment of inertia I (the density of the object is not uniform). With your hand you pull the string straight up with some constant force F such that the center of the object does not move up or down, but the object spins faster and faster (Figure 9,62). This is like ay0-y0; nothing but the vertical string touches the object.


When your hand is a heighty0above the floor, the object has an angular speed蝇0. When your hand has risen to a height y above the floor, what is the angular speed蝇of the object? Your result should not containFor the (unknown) radius of the object. Explain the physics principles you are using.

A sphere or cylinder of mass M, radius R and moment of inertia I rolls without slipping down a hill of height h, starting from rest. As explained in problem P.33, if there is no slipping 蝇=vCM/R. (a) In terms of given variables (M,R,I and h), what is VCM at the bottom of hill? (b) If the object is a thin hollow cylinder, what is VCM at the bottom of hill? (c) If the object is a uniform density hollow cylinder, ), what isVCM at the bottom of hill? (d) If the object is a uniform density sphere what is VCM at the bottom of hill? An interesting experiment that you can perform that is to roll various objects down an inclined board and see how much time each one takes to reach the bottom.

Discuss qualitatively the motion of the atoms in a block of steel that falls onto another steel block. Why and how do large-scale vibrations damp out?
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