1. How much acceleration does a 747 jumbo jet of mass 31600 kg experience in takeoff when the thrust for each of four engines is 30000 N?
2. Two boxes are seen to accelerate at the same rate when a force F is applied to the first and 5F is applied to second. What is the mass ratio of the boxes?
1.) a=f/m; f= 30,000 N and m= 30,000 kg; you must do 30,000 N * 4 = 120,000 N because there are 4 jets that are each 30,000 N; a= 120,000 N / 30,000 kg = 4 m/s^2
(4 x 30000)/31600 should get you your answer to 1
1. Well, let's put it this way: A jumbo jet's acceleration during takeoff is so impressive, it could give Usain Bolt a run for his money! But to answer your question seriously, we can use Newton's second law, which states that force equals mass times acceleration (F = ma). So, if the thrust for each engine is 30,000 N and there are four engines, then the total force would be 4 * 30,000 N = 120,000 N. Now we can rearrange the equation to solve for acceleration (a = F/m). Plugging in the values, we get a = 120,000 N / 31,600 kg, which is approximately 3.8 m/s². That's some serious acceleration!
2. Ah, the classic case of "acceleration and the box buddies." When a force F is applied to the first box and 5F is applied to the second box, we know that both boxes accelerate at the same rate. Let's call their masses m₁ and m₂, respectively. According to Newton's second law, the force on the first box is F = m₁a and the force on the second box is 5F = m₂a. Since both boxes have the same acceleration, we can set these two equations equal to each other: m₁a = 5F. Dividing both sides by F, we find that m₁ = 5. So, the mass ratio of the boxes is 5:1. Looks like the second box is feeling the love... or force, in this case!
To find the acceleration of the 747 jumbo jet during takeoff, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for calculating acceleration is:
acceleration = net force / mass
1. For the first question, the net force acting on the 747 jumbo jet can be calculated by multiplying the thrust of each engine by the total number of engines. Given that there are four engines and each engine has a thrust of 30,000 N, the total net force is:
net force = 4 * thrust per engine = 4 * 30,000 N
Next, we can substitute the values into the formula:
acceleration = net force / mass
acceleration = (4 * 30,000 N) / 31,600 kg
By evaluating the expression, we can find the acceleration experienced by the 747 jumbo jet during takeoff.
2. For the second question, we need to determine the mass ratio of the two boxes when they both experience the same acceleration. Since acceleration is the same for both boxes, we can equate the two formulas for acceleration:
F₁ / m₁ = F₂ / m₂
Given that the force applied to the first box (F₁) is F and the force applied to the second box (F₂) is 5F, we can substitute these values into the equation:
F / m₁ = 5F / m₂
Next, we can simplify the equation by canceling out the common factor of F:
1 / m₁ = 5 / m₂
To find the mass ratio, we can invert both sides of the equation:
m₁ / 1 = m₂ / 5
So, the mass ratio of the boxes is 1:5.
1. F = 4 * 30000N = 120000N.
F = ma = 120000,
31600*a = 120000,
a = 120000 / 31600 = 3.8 m/s^2.
2. F = ma,
m1 = F/a,
m2 = 5F/a,
m2/m1 = (5F/a) / (F/a) = 5F/a * a/F =
5F/F = 5/1.