The thrust of a certain model rocket engine as a function of time is shown below. Here, the word "thrust" refers to the force by the exhaust on the rocket as the rocket engine is firing.

Figure: The thrust curve of a certain model rocket engine.

The total area under the curve is 1.84 N s. The total burn time of the rocket engine is 1.24 s. The peak thrust has a magnitude 8.60 N. Since force is a vector, assume that the thrust is in the +y direction.

Calculate the average thrust on the rocket due to the rocket engine.

Compare the average thrust to the peak thrust. Explain why the average thrust is so much smaller than the peak thrust.

If the thrust by the rocket engine on the rocket is the only force acting on the rocket, then what will be the change in the rocket's momentum during the time interval from t=0 to t=1.24 s?

1220004 Change in momentum of Earth in 1 day during its orbit around Sun 1220004

Earth orbits Sun in a nearly circular orbit with a speed m/s. Suppose that at a certain instant, Earth's velocity is in the –x direction. At this instant, the force by Sun on Earth is . What will be Earth's momentum 1 day later? During this time interval, the only significant force acting on Earth is the gravitational force by Sun on Earth.

Figure: The gravitational force by Sun on Earth.

1220002 Impulse on an alpha particle by a gold nucleus (Rutherford scattering) 1220002

An alpha particle has a speed of m/s in the +x direction when it collides with a gold nucleus. and deflects at an angle above the +x axis. Its speed after the collision nearly the same as its speed before the collision because the gold nucleus is so massive compared to the alpha particle. What is the impulse on the alpha particle due to the collision with the gold nucleus?

While playing air hockey, the puck comes toward you with a speed of 0.8 m/s at an angle of above the –x axis. You strike it with your paddle, and after the collision, the puck travels in the +x direction with a speed of 2 m/s toward the opponent's goal. The mass of the puck is 0.020 kg.

Figure: An air hockey puck before being struck by the air hockey paddle.

What was the impulse on the puck?

What is the direction of the net force on the puck during the collision?

What must be measured if you want to calculate the net force on the puck during the collision?

1220005 Impulse on a proton at relativistic speeds in the LHC 1220005

What impulse is required to accelerate a proton of mass from 0.95c to 0.99999999c (which is the maximum speed achieved with the Large Hadron Collider)? Assume that the proton travels along a straight line in the +x direction.

1150002 Magnitude and direction of a velocity vector 1150002

The picture shows a 0.4-kg football after it is thrown. The ball is traveling from left to right in the picture. On the picture, sketch the initial position vector , the final position vector and the displacement vector for the football.