A Few questions- please help!!! also show steps!
What magnitude of force, acting for 0.025 s, will change the velocity of a 100 g ball from 30 m/s eastward to 40 m/s westward?
A girl holds a 1.7 kg air rifle loosely and fires a bullet of mass 2 g. The muzzle velocity of the bullet is 160 m/s. What is the magnitude of the recoil velocity of the gun?
An astronaut of mass 70 kg carries an empty oxygen tank of mass 14 kg. He throws the tank away from himself with a speed of 3 m/s. With what velocity does the astronaut start to move through space?
Two carts are stationary with a compressed spring between them. When the spring is released, the two carts move apart. After the spring is released, one cart m = 3 kg has a velocity of 0.74 kg m/s east. What is the magnitude of the velocity of the second cart (m = 1.7kg) after the spring is released?
In a freight yard a train is being made up. An empty freight car, coasting at 9 m/s, strikes a loaded car that is stationary, and the cars couple together. Each of the cars has a mass of 3200 kg when empty, and the loaded car contains 13000 kg of bottled soft drinks. With what speed does the combined mass start to move?
A cart with a mass of 0.6 kg moving at 4 m/s collides with a stationary cart that has a mass of 0.6 kg. If the two carts stick together after the collision, what is the final velocity?
A rock (m = 1.5 kg) moving at 4.2 m/s north collides with a ball (m = 0.061 kg) that is initially at rest. What is the velocity of the rock after the collision if the velocity of the ball after the collision was 8.4 m/s north?
A 45 kg cart is moving across a frictionless floor at 1.7 m/s. A 60 kg boy, riding in the cart, jumps off the cart so that he hits the floor moving forwards in the initial direction of the cart's motion with a velocity of 2.8 m/s. What is the velocity of the cart after the boy jumped?
change in velocity = 70
force * time = change in momentum (or impulse)
F * .025 = 0.100 * 70
The next one is conservation of momentum. I am not going to do them all for you. You try.
Sure! I'll provide step-by-step explanations for each of the questions you have asked.
1. To find the magnitude of force, you can use the equation F = (m * Δv) / Δt, where F is the force, m is the mass, Δv is the change in velocity, and Δt is the time taken.
Given:
Mass (m) = 100 g = 0.1 kg
Initial velocity (u) = 30 m/s eastward
Final velocity (v) = 40 m/s westward
Time (Δt) = 0.025 s
First, calculate the change in velocity:
Δv = v - u = 40 m/s - (-30 m/s) = 70 m/s
Now, substitute the values into the formula and solve for force:
F = (0.1 kg * 70 m/s) / 0.025 s
F = 280 N
Therefore, the magnitude of force needed is 280 N.
2. The recoil velocity of the gun can be found using the law of conservation of momentum. According to this law, the total momentum before firing should be equal to the total momentum after firing.
Given:
Mass of the gun (m1) = 1.7 kg
Mass of the bullet (m2) = 2 g = 0.002 kg
Muzzle velocity of the bullet (v1) = 160 m/s
Recoil velocity of the gun (v2) = ?
First, calculate the momentum before firing:
Initial momentum (before firing) = m1 * 0 + m2 * v1 = 1.7 kg * 0 + 0.002 kg * 160 m/s = 0.32 kg·m/s
According to the law of conservation of momentum, the momentum after firing should be equal to the initial momentum:
Final momentum (after firing) = m1 * v2 + m2 * 0 = 1.7 kg * v2 + 0.002 kg * 0 = 1.7 kg * v2
Equating the initial and final momentum:
0.32 kg·m/s = 1.7 kg * v2
Solve for v2:
v2 = 0.32 kg·m/s / 1.7 kg
v2 ≈ 0.1882 m/s
Therefore, the magnitude of the recoil velocity of the gun is approximately 0.1882 m/s.
3. The velocity of the astronaut after throwing the tank can be found using the law of conservation of momentum. The initial momentum (before throwing the tank) should be equal to the final momentum (after throwing the tank).
Given:
Mass of the astronaut (m1) = 70 kg
Mass of the tank (m2) = 14 kg
Initial velocity of the astronaut (v1) = ?
Final velocity of the astronaut (v2) = 3 m/s (opposite direction of thrown tank)
First, calculate the initial momentum:
Initial momentum = m1 * v1 = 70 kg * v1
According to the law of conservation of momentum:
Initial momentum (before throwing tank) = Final momentum (after throwing tank)
m1 * v1 = (m1 + m2) * v2
Solve for v1:
v1 = (m1 + m2) * v2 / m1
v1 = (70 kg + 14 kg) * (-3 m/s) / 70 kg
v1 ≈ -0.2571 m/s
Therefore, the velocity of the astronaut after throwing the tank is approximately -0.2571 m/s (opposite direction of initial motion).
The remaining questions will be answered in subsequent responses to avoid exceeding the character limit.