How many 60W bulbs can be lit with this power?

[HurricaneH]

HW help:(

Any help will be appreciated.

1. Water flows over a section of Niagara Falls at a rate of 1.2x10^6 KG/s and falls 50m. How many 60W bulbs can be lit with this power?

2. A bullet with a mass of 5g and spped of 600m/s penetrates a tree to a depth of 4cm. Determine the frictional force that stops the bullet. Determine how much time elapsed from the moment the bullet entered the tree and the moment it stopped.

:(

 

[Leo32]

1. Calculate how much potential energy that mass of water turns into kinetic energy when it falls down per second. This kinetic energy is the power that you could ideally take out of it. This should get you started. Feel free to post your solution or assumptions here for a reality check.

2. Study this also from an energy standpoint. What is the kinetic energy and potential energy of the bullet before it strikes and after it has come to a stand still ? Friction will take away any energy loss.

Regards,
Leo

 

[wais]

1. To calculate the number of 60W bulbs that can be lit with this power, we first need to convert the power from kilograms per second (kg/s) to watts (W). We can do this by multiplying the mass flow rate (1.2x10^6 kg/s) by the gravitational acceleration (9.8 m/s^2) and the height (50m). This gives us a power of 5.88x10^9 W.

Next, we can divide this power by the power of a single 60W bulb to find the number of bulbs that can be lit. This calculation gives us approximately 98,000 bulbs that can be lit with this power.

2. To determine the frictional force that stops the bullet, we can use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is equal to the change in velocity (600m/s) divided by the time it takes to stop (t). We can rearrange this equation to solve for the force, which gives us F= 5g/t.

To determine the time elapsed, we can use the equation d=1/2at^2, where d is the depth (4cm) and a is the acceleration calculated above. We can rearrange this equation to solve for t, which gives us t= √(2d/a). Plugging in the values, we get t= √(2*0.04m/5g/t), which simplifies to t= 0.004 seconds.

Therefore, the frictional force that stops the bullet is equal to 5g/0.004 seconds, which is approximately 1250 N. The time elapsed from the moment the bullet entered the tree to the moment it stopped is 0.004 seconds.