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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 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’s 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·m/s20.3kg=60.3·1kg·m/s21kg=60.3·1m/s2=20m/s2

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

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Most popular questions from this chapter

A rod of length Land negligible mass is attached to a uniform disk of mass Mand radius R (Figure 9.64). A string is wrapped around the disk, and you pull on the string with a constant force F . Two small balls each of mass mslide along the rod with negligible friction. The apparatus starts from rest, and when the center of the disk has moved a distance d, a length of string shas come off the disk, and the balls have collided with the ends of the rod and stuck there. The apparatus slides on a nearly frictionless table. Here is a view from above:

(a) At this instant, what is the speed vof the center of the disk? (b) At this instant the angular speed of the disk isω . How much internal energy change has there been?

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 ω=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.

A runner whose mass is 50 kgaccelerates from a stop to a speed of10 m / s in 3 s. (A good sprinter can run100 m in about 10 s, with an average speed of 10 m / s.) (a) What is the average horizontal component of the force that the ground exerts on the runner’s shoes? (b) How much displacement is there of the force that acts on the sole of the runner’s shoes, assuming that there is no slipping? Therefore, how much work is done on the extended system (the runner) by the force you calculated in the previous exercise? How much work is done on the point particle system by this force? (c) The kinetic energy of the runner increases—what kind of energy decreases? By how much?

A chain of metal links with total mass M = 7 kg is coiled up in a tight ball on a low-friction table (Figure 9.52). You pull on a link at one end of the chain with a constant force F= 50 N. Eventually the chain straightens out to its full length = 2.6 m. and you keep pulling until you have pulled your end of the chain a total distance d=4.5 m.

(a) Consider the point particle system. What is the speed of the chain at this instant? (b) Consider the extended system. What is the change in energy of the chain? (c) In straightening out, the links of the chain bang against each other, and their temperature rises. Assume that the process is so fast that there is insufficient time for significant transfer of energy from the chain to the table due to the temperature difference, and ignore the small amountof energy radiated away as sound produced in the collisions among the links. Calculate the increase in internal energy of the chain.

Three uniform-density spheres are positioned as follows:

  • A3kg sphere is centered at <10,20,-5>m.
  • A 5kgsphere is centered at <4,-15,8>m.
  • A 6kgsphere is centered at <-7,10,9>m.

What is the location of the center of mass of this three-sphere system?
See all solutions

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