You (m = 50 kg) are in a rollercoaster travelling at a constant speed of 50 mph when it goes over a hump which, at the top, can be approximated by a circle of radius 15 m. (A) Is the harness necessary in order for you to stay on the ride? In other words, if there was nothing keeping you in your seat, would you fly off? (B) If you answer to (A) is no, calculate the normal force at the top, if your answer to (A) is yes, calculate the force the harness must exert on you. (Remember that force is a vector so you have to indicate direction as well.) Hint for (A): 1. With what speed would you have to go over the hump in order for only gravity to be needed? 2. If your speed is larger, what do you think is going on?

An object is thrown upward with a speed of 15.2 m/s on the surface of planet X where the acceleration due to gravity is 1.8 m/s². What is the maximum height reached by the object? Answer: Check

(a) How far from the center of Earth would the net gravitational force of Earth and the Moon on an object be zero? (b) Setting the magnitudes of the forces equal should result in two answers from the quadratic. Do you understand why there are two positions, but only one where the net force is zero?

In an amusement park ride, riders stand against the wall of a spinning cylinder. The floor falls away and the riders are held up by friction. If the radius of the cylinder is 4 m, find the minimum number of revolutions per minute necessary when the coefficient of friction between a rider and the wall is 0.4.

In the below figure, we have listed data taken from a fictional planet. Aprojectile has been launched horizontally, and its height from the groundhas been measured at different times.(a) Draw a linear plot of h so that h is on the vertical axis.(b) Estimate the gravitational acceleration of this planet time(s)           h(m) 1.0                 190 2.0                 160 3.0                 110 4.0               40

At the surface of planet X, a 1 kg object weighs 4 N (planet radius R=106m). A space probe passes by planet X with the nearest point (A) at 8R from the center. When the probe was very far away it had a speed of sqrt(2gxR), where gx is the acceleration of gravity at the planet surface. Find a value for the speed of this probe when it is at point A, vA.

A roller-coaster car has a mass of 513 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and- down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius ₁ = 10.0 m 15.0 m, respectively. and r2 = B (a) If the vehicle has a speed of 19.9 m/s at point, what is the force exerted by the track on the car at this point? N (b) What is the maximum speed the vehicle can have at B and still remain on the track? m/s

A race car goes around a level, circular track with a radius of 22 meters at a constant speed of 39.6 m/s.(a) What is the car's centripetal acceleration?