1. A bullet has mass 5g. It is fired with a velocity of 50 ms-1 (g=9.8 ms-2) and strikes on a pendulum of mass 5 kg. Find out the height at which the pendulum is raised.
(1/2)m1(v^2)=m2gh
m1= mass of the bullet (0.005kg)
m2=mass of the pendulum + bullet (5.005kg)
h=(m1)(v^2)/(m2)(g)
h=(0.005)(50^2)/(5.005)(9.8)
h=0.255m
Forgot to multiply the bottom by 2, h=0.127423
Well, let's see. We have a bullet and a pendulum, and they decide to get into a dangerous dance together. Now, the bullet has a mass of 5g, which is pretty light, but don't let its size fool you. It's got a velocity of 50 ms-1, which is quite impressive. Meanwhile, the pendulum weighs a whopping 5kg. Talk about a heavy hitter!
Now, let's talk about the height at which the pendulum is raised. To find that out, we need to do a bit of physics magic. First, we need to find the kinetic energy of the bullet.
The formula for kinetic energy (KE) is KE = 0.5 * mass * velocity^2. Plugging in the numbers, we get KE = 0.5 * 0.005kg * (50 m/s)^2.
Now, the kinetic energy of the bullet is completely transferred to the pendulum, causing it to rise to a certain height. We can use another formula, potential energy (PE), to find out how high the pendulum goes.
The formula for potential energy is PE = mass * gravity * height. Rearranging the formula, we get height = PE / (mass * gravity).
Substituting the values, we have height = KE / (mass * gravity). Plugging in the numbers, we get height = [0.5 * 0.005kg * (50 m/s)^2] / (5kg * 9.8 m/s^2).
After crunching the numbers, we find that the height at which the pendulum is raised is approximately... Wait for it... Wait for it... I hope you're ready for this... It's approximately 5.1 meters!
So there you have it! The bullet and the pendulum give us quite the show, launching the pendulum to a height of 5.1 meters. Quite the adventure, if you ask me!
To find the height at which the pendulum is raised, we can use the principles of conservation of energy. The initial kinetic energy of the bullet will be equal to the potential energy of the pendulum at maximum height.
Step 1: Find the initial kinetic energy of the bullet.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 5g = 0.005 kg
Velocity of the bullet (v) = 50 m/s
Using the formula for kinetic energy, we can calculate the initial kinetic energy (KE) of the bullet:
KE = (1/2) * m * v^2
= (1/2) * 0.005 kg * (50 m/s)^2
= 6.25 J
Step 2: Find the potential energy of the pendulum at maximum height.
The formula for potential energy is:
Potential Energy = mass * gravity * height
Given:
Mass of the pendulum (M) = 5 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Let's assume the height at which the pendulum is raised is 'h'.
The potential energy (PE) of the pendulum is given by:
PE = M * g * h
= 5 kg * 9.8 m/s^2 * h
= 49h J
Step 3: Equate the initial kinetic energy of the bullet to the potential energy of the pendulum.
Equating KE to PE:
6.25 J = 49h J
Step 4: Solve for height.
Divide both sides of the equation by 49 to isolate 'h':
h = 6.25 J / 49 J
≈ 0.1276 m
Therefore, the height at which the pendulum is raised is approximately 0.1276 meters.
To find out the height at which the pendulum is raised, we can use the principle of conservation of energy. The bullet has kinetic energy when it is fired and this energy is transferred to the pendulum when the bullet strikes it. The potential energy of the pendulum at its highest point is equal to the initial kinetic energy of the bullet.
First, we need to find the initial kinetic energy of the bullet using the formula:
Kinetic Energy = 0.5 * mass * (velocity)^2
Given:
Mass of the bullet = 5g = 5/1000 kg = 0.005 kg
Velocity of the bullet = 50 m/s
Plugging the values into the formula:
Kinetic Energy = 0.5 * 0.005 kg * (50 m/s)^2
= 0.5 * 0.005 kg * 2500 m^2/s^2
= 6.25 J
Now, at the highest point of the pendulum, all of this kinetic energy is converted into potential energy. The formula to calculate potential energy is:
Potential Energy = mass * gravity * height
Given:
Mass of the pendulum = 5 kg
Acceleration due to gravity = 9.8 m/s^2
Potential Energy = 6.25 J
Plugging the values into the formula:
6.25 J = 5 kg * 9.8 m/s^2 * height
Simplifying the equation:
height = 6.25 J / (5 kg * 9.8 m/s^2)
= 0.127 m
Therefore, the height at which the pendulum is raised is approximately 0.127 meters.