A problem involves a car of mass m going down a track from a height H,...

A problem involves a car of mass m going down a track from a height H, and round a loop of radius r. The loop is frictionless.

It asks for the minimum cut-off speed required, at the highest point in the loop (call it point D), such that the car makes it round the loop without falling. I know the solution; I should set the centripetal accleration equal to 9.81. In other words, contact force with the track at point D is equal to zero.

But I tried solving it by conservation of energy. At point D, the car is at a height 2r from ground level. Therefore, in order for the car to reach that height at point D, it must initially have a potential energy of mg(2r). Meaning, it should be released from a height H = 2r.

I got the wrong answer and I'm confused why that happened. Isn't that how conservation of energy work? Please clarify, where's the error in my solution?

Expert Solution

genius_generous answered 1 year ago

A container with mass m kg is dropped by a helicopter from height h km at...

A container with mass m kg is dropped by a helicopter from height h km at time t=0, with zero velocity. from the outset, its fall is controlled by gravity and the force of air resitance, f(v)= -kv, where v is the current velocity of the container. in t seconds after the drop, a parachute opens, resulting in an increase of air resistance up to f(v) = -kv. determine the time t at which the container touches the ground. and...

The mass m is dropped from a height h. Find the magnitude of Coriolis deflection and...

The mass m is dropped from a height h. Find the magnitude of Coriolis deflection and its direction (i.e north south east or west). You can assume location being in the northern hemisphere at latitude θ and that rotation of the Earth is slow.

Two solid spheres are running down from incline of height 3.7 m. Sphere A has mass...

Two solid spheres are running down from incline of height 3.7 m. Sphere A has mass 3.3 kg; radius 15.7 cm; sphere B has mass 7.4 kg and radius of 39.3 cm. Find the ratio of their angular velocities omegaA/omegaB at the bottom of the incline.

Chapter 08, Problem 024. A block of mass m = 1.30 kg is dropped from height...

Chapter 08, Problem 024. A block of mass m = 1.30 kg is dropped from height h = 59.0 cm onto a spring of spring constant k = 1130 N/m (see the figure). Find the maximum distance the spring is compressed.

A roller-coaster car is starting from rest from the top of the slope of height H....

A roller-coaster car is starting from rest from the top of the slope of height H. As it reaches the bottom of the slope, it is moving at 30 m/s along a straight horizontal track. Using the principle of conservation of energy, a. Calculate the height H. b. Calculate the speed of the roller-coaster car after climbing the 10 m hill shown in the figure. Ignore friction. c. What is the change in kinetic energy as the car goes a....

A 12,000 N car starts from rest and rolls down a hill from a height of...

A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail. (a) Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of 1.2 106 N/m. ? m (b) Calculate the maximum acceleration of the car after contact with the spring,...

A ball rolls down from the top of an incline with a height of 5 m...

A ball rolls down from the top of an incline with a height of 5 m high without slipping. The ball has a diameter of 0.2m. What are the ball’s translational speeds a) at the center of the ball, b) at the contact point on the ground, and c) at the top of the ball when it arrives at the bottom? What values of "c" do you expect for hollow/solid balls? Will the hollow ball be faster?

A car of mass 500 kg is going towards east at 20.0 m/s. It hits a...

A car of mass 500 kg is going towards east at 20.0 m/s. It hits a slow moving truck (moving at speed 10.0 m/s also going towards east) of mass 2000 kg from back. (a) If after the collision the truck is moving at 15.0 m/s towards east, what is the velocity of the car? (b) If the collision between the car and the truck is perfectly elastic, find their velocities after the collision. (c) Find the percentage loss of...

a 15 kg rock slides down a frictionless icy hill of height h= 20.0 m, starting...

a 15 kg rock slides down a frictionless icy hill of height h= 20.0 m, starting at the top of speed on the ground that offers kinetic v0 = 9m/s. Once it reaches the bottom (Point C) it continues horizontally on the ground that offers kinetic friction with uk=0.2. After traveling a distance = 110m to reach point D, it begins compressing a spring with spring constant 2 N/m a. what is the speed of the rock when it reaches...

Use proper calculus. (a) A conical shell has mass M, height h, and base radius R,...

Use proper calculus. (a) A conical shell has mass M, height h, and base radius R, Assume it is made from thin sheet of uniform thickness, Derive its center of mass and moment of inertia about its symmetry axis. (b) Derive the formula for the center of mass and the moment of inertia of a solid sphere, and then that of the moment of inertia about an axis tangent to the surface. (c) Derive the formula for the moment of...

Question