How Many Rocks Must a Child Throw to Maintain Constant Speed in a Wagon?

[bkoz316]

Remain at constant speed?

A child sits in a wagon with a pile of 0.47 kg rocks. If she can throw each rock with a speed of 9 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per minute to maintain a constant average speed against a 3.5 N force of friction?



Not sure on what to do...please help!


Thanks!

 

[PhanthomJay]

A child sits in a wagon with a pile of 0.47 kg rocks. If she can throw each rock with a speed of 9 m/s relative to the ground, causing the wagon to move, how many rocks must she throw per minute to maintain a constant average speed against a 3.5 N force of friction?



Not sure on what to do...please help!


Thanks!

You have to determine what force the child must exert the wagon in order to make it move at constant speed. Then that force can be equated to the momentum change caused by the changing mass (Hint: F= rate of change of momentum, per Newton's 2nd law).

 

[ogb p]

I would recommend using the equation for Newton's second law, F=ma, to solve this problem. First, we need to find the total mass of the wagon and rocks, which would be 0.47 kg for the rocks plus the mass of the wagon (let's say 5 kg for a total of 5.47 kg). Then, we can use the given force of friction (3.5 N) and divide it by the total mass to find the acceleration (a=3.5 N/5.47 kg=0.64 m/s^2).

Next, we can use the equation for constant speed, v=at, where v is the speed, a is the acceleration, and t is the time. Since we want to maintain a constant speed, we can set v=9 m/s, a=0.64 m/s^2, and solve for t.

9 m/s=0.64 m/s^2 * t
t=14.06 seconds

This means that for every 14.06 seconds, the child must throw enough rocks to maintain the wagon's speed. To find how many rocks she needs to throw per minute, we can use the conversion 60 seconds=1 minute.

(60 seconds/14.06 seconds) * (1 rock/14.06 seconds) = 4.27 rocks per minute

Therefore, the child must throw approximately 4 rocks per minute to maintain a constant average speed against the force of friction. However, this calculation assumes that the force of friction remains constant. In reality, the force of friction may change depending on various factors such as the surface of the ground or the condition of the wagon's wheels. To truly maintain a constant speed, the child may need to adjust the number of rocks thrown per minute accordingly.