A pallet of boxes weighing 10 tons is dropped from a lift truck from a height of 10 feet. The maximum velocity the pallet attains before hitting the ground is 6 ft/s. How much kinetic energy does the pallet have in (ft)(lbf) at this velocity?
An object dropped from 10 feet should acquire a velocity quite a bit higher than 6 ft/s, before impact. This problem is presenting conflicting data.
Perhaps they want you to use
(1/2) M V^2 for the kinetic energy. The mass would have to be
M = W/g = 20,000 /32.2 = 621 slugs
if you want the answer in ft-lbf
To calculate the kinetic energy of the pallet, we can use the equation:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
First, we need to convert the weight of the pallet from tons to pounds. Since 1 ton is equal to 2000 pounds, the weight of the pallet in pounds is:
Weight = 10 tons * 2000 lb/ton = 20,000 lb
Next, we convert the height from feet to inches since we are dealing with weight in pounds:
Height = 10 feet * 12 inches/feet = 120 inches
The potential energy (PE) of the pallet at this height can be calculated as:
Potential Energy (PE) = Weight * Height
PE = 20,000 lb * 120 inches = 2,400,000 in-lb
Now we can calculate the velocity of the pallet in feet per second (ft/s):
Velocity = 6 ft/s
Finally, using the formula for kinetic energy, we can calculate the kinetic energy of the pallet:
KE = 0.5 * weight * velocity^2
KE = 0.5 * 20,000 lb * (6 ft/s)^2
KE = 0.5 * 20,000 lb * 36 ft^2/s^2
Calculating the above expression:
KE = 360,000 ft-lbf
Therefore, the kinetic energy of the pallet at this velocity is 360,000 ft-lbf.
To calculate the kinetic energy of the pallet, we can use the formula:
Kinetic energy (KE) = (1/2) * mass * velocity^2
First, let's convert the weight of the pallet from tons to pounds. Since 1 ton is equal to 2000 pounds, the pallet weighs 10 tons * 2000 pounds/ton = 20,000 pounds.
Next, let's convert the height from feet to inches. Since there are 12 inches in a foot, the height is 10 feet * 12 inches/foot = 120 inches.
We can calculate the potential energy of the pallet at that height using the formula:
Potential energy (PE) = mass * gravity * height
Since gravity is approximately 32.2 ft/s^2, the PE = 20,000 pounds * 32.2 ft/s^2 * 120 inches * (1 foot/12 inches) = 7,230,857.14 ft-lbf.
At the maximum velocity of 6 ft/s, the pallet has converted all of its potential energy into kinetic energy. Therefore, the kinetic energy (KE) is equal to the potential energy at that height.
So, the kinetic energy (KE) = 7,230,857.14 ft-lbf.