Solving Block B's Stop Time: A 1-lb Ball & 10-lb Block

[danyalasdf]

Homework Statement

A 1-lb ball A is traveling horizontally at 20 ft/s when it strikes a 10-lb block B that is at rest. If the coefficient of restitution between A and B is e = 0.6, and the coefficient of kinetic friction between the plane and the block is µk = 0.4, determine the time for the block B to stop sliding.

The Attempt at a Solution

M1V1=M2V2

(1/32.2)(20) + 0 = (1/32.2)(Va2) + (10/32.2)(Vb2)

(Va2) + 10(Vb2) = 20

e = (Vb2-Va2)/(Va1-Vb1)

0.6 = (Vb2-Va2)/(20-0)

(Vb2 - Va2) = 12

From here I get that

Vb2 = 2.909 ft/s to the right

Va2 = -9.091 ft/s to the left

Block B

T1 + U(1→2) = T2

this where I am stuck ?

any help?

 

[TSny]

So, you need to find the distance B slides. You know the initial speed of B at the beginning of the slide and you know it will slide until it comes to rest.

You can either use energy concepts to get the distance of slide, or you can use Newton's second law to find the deceleration during the slide and then use kinematic equations to find the distance.

If you use energy concepts then you would think about the relationship between the work done by the force of friction and the change in kinetic energy.

 

[danyalasdf]

no, that i need help to determine the time for the block B to stop sliding.

 

[TSny]

Sorry. I misread the question. I would suggest finding the deceleration and using kinematic equations.

 

[Nickie]

I would first start by clarifying the question and making sure all the units are consistent. The given information states that the ball A is traveling horizontally at 20 ft/s, but in the attempted solution, it is written as 20-0, which is not a valid unit for velocity. Additionally, the initial velocity for the block B is not given, so it cannot be assumed to be zero.

To solve this problem, the equations of motion can be used. The first step would be to find the acceleration of the block B by using Newton's Second Law, F = ma. In this case, the only force acting on the block is the frictional force, which is given by µkmg. The mass of the block is 10 lbs, and the acceleration can be found by dividing this force by the mass.

Next, the equations of motion can be used to find the time for the block to stop sliding. The initial velocity for the block B is not given, so it will have to be calculated using the equation v^2 = u^2 + 2as, where u is the initial velocity, v is the final velocity (which is zero in this case), a is the acceleration, and s is the distance traveled. The distance traveled can be found by using the equation s = ut + 1/2at^2, where t is the time.

Once the initial velocity is known, the time can be calculated using the equation t = (v-u)/a. This will give the time for the block to stop sliding.

It is important to note that the coefficient of restitution does not affect the motion of the block B, as it only applies to the collision between the ball A and the block B. The coefficient of kinetic friction, on the other hand, does affect the motion of the block B and needs to be taken into account in the calculations.

In conclusion, to determine the time for the block B to stop sliding, the equations of motion can be used by finding the acceleration of the block B and using it to calculate the time. It is important to use consistent units and to take into account all the given information, including the coefficient of kinetic friction.