Newton hypothesized that a cannonball fired parallel to the ground from a cannon on the surface of the Earth would orbit Earth if it had sufficient speed and if air friction were ignored.
a) What speed would the cannonball have to have to do with this? (Use Kepler's Third Law)
b) If the mass of the cannonball were doubled, what time would it take to orbit Earth once?
Newton hypothesized that a cannonball fired parallel to the ground from a cannon on the surface...
Newton’s Cannon Imagine you fired a cannonball such that the range of that ball was slightly longer than the radius of the Earth. As that ball fell back down, it would miss the ground and continue to fall. If we can ignore any air resistance or collisions with other objects, then we can say the ball would continue to fall forever, just missing the ground, and thus be in orbit. Assume all orbits here are perfectly circular and pretend that...
A cannonball is fired from a cannon at ground level at an angle of 44° above the horizontal with an initial speed of 32.0 m/s. What is the maximum height reached by the cannonball? (with steps and explanation)
A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 70.0m above ground level, and the ball is fired with initial horizontal speed v0. Assume acceleration due to gravity to be g = 9.80m/s2 . Part A Assume that the cannon is fired at time t=0 and that the cannonball hits the ground at time tg. What is the y position of the cannonball at the time tg/2? Answer is 52.5 Part...
A cannon shoots a cannonball from the ground level (ignore the height of the cannon) towards a cliff of height h = 170 m. The cannonball is launched with an initial velocity of 110 m/s at an angle of 64° above the horizontal. Neglect air resistance. Assume the cannonball hits the cliff as it descends (on its way down) exactly at the edge, as shown. a. Determine the maximum height above the ground reached by the cannonball.b. What speed will the...
Homework H.4.M Given: A cannonball P of mass m is fired toward a steel barrier on a stationary cart. At some time after rebounding from the barrier, the cannonball is observed to have a speed of up and is moving in the direction shown below in the figure. Let M be the combined mass of the cannon/cart. Assume that the cart is able to move without friction along the horizontal surface and ignore the influence of air resistance. Find: For...
Newton's Thought Experiment In the seventeenth century, Sir Isaac Newton was studying the nature of motion and gravity. He formulated a thought experiment that would eventually become the basis of the development of satellites. Imagine an object is fired from a cannon horizontal to the plane of the earth. The projectile will travel in a horizontal direction and undergo projectile motion as gravity begins to pull the projectile downward However, the earth is a sphere, which means as the projectile...
(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 4.98 104 m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) (b) What If? The speed provided in part (a) is very difficult to achieve...
A 0.2 kg cannon ball is fired at an upward angle of 45° from the top of a 165 m cliff with a speed of 175 m/s. (A) Using conservation of energy, find the speed it has when it strikes the ground below. Suppose the cannon ball lands in a soft, muddy field. The force of the field is 75 N on the projectile. (B) How deep does it penetrate into the ground? -------------------------------------------------------------------------------- How much energy does it take...
Derive Kepler's 2^nd law from conservation of angular momentum Derive Kepler's 3^rd law from Newton's laws of motion and gravitation for a circular tool You have landed a job with Space X as a space physicist. Your first job is to launch a satellite. The plan is to lift off from the surface of the Earth and then insert the satellite into an elliptical transfer orbit with its perigee at A and apogee at A'. The spacecraft will be unpowered...
AHHA Summing Up PART A: NEWTON'S CANNON 1. Acannonball dropped from a cliff will fall straight down and hit the surface of the Earth. How could the cannonball be made to orbit the Earth instead? waHTRo Based on your experience with the simulation, which do you think is more common: circular orbits or noncircular elliptical orbits? Defend your answer 2. PART B: HARMONY OF THE WORLDS 3. Use the following method to determine the relationship between the orbital radius of...