A mass m slides down a frictionless ramp and approaches a frictionless loop with radius R....

A mass m slides down a frictionless ramp and approaches a frictionless loop with radius R. There is a section of the track (between the ramp and the loop) with length 2R that has a kinetic friction coefficient of 0.5. From what height h must the mass be released to stay on the track? No figure.

1.5R 2.5R 3.5R 4.5R or 5.5R

Solutions

Expert Solution

We will study this motion into three parts:

First the friction-less ramp, the track of length 2R and friction-less loop of radius R.

We consider the problem on the basis of law of Energy conservation. As the ramp is friction-less the energy will remain mgh and friction will reduce it's energy.

h=3.5R

#Hi, I am providing you the detailed solution for the question you have asked. If you are happy and find this useful please thumbs up. In case, if you have any query regarding the solution please let me know in the comments section below. Thanks!!

genius_generous answered 9 months ago

Next > < Previous

Related Solutions

A box (with a penguin inside) with mass, M, slides down a frictionless ramp, starting a...

A box (with a penguin inside) with mass, M, slides down a frictionless ramp, starting a height H above ground level. At the lowest point of the ramp (height = -0.1H) it slides through a curved section of track with radius, R= 0.25H. The box (w/ penguin) then rises to ground level (height = 0) and at that point, leaves a jump at an angle θ. At the highest point of its trajectory, h2, it strikes a blob of glue...

A cart of mass m1 = 11 kg slides down a frictionless ramp and is made...

A cart of mass m1 = 11 kg slides down a frictionless ramp and is made to collide with a second cart of mass m2 = 24 kg which then heads into a vertical loop of radius 0.25 m (a) Determine the height h at which cart #1 would need to start from to make sure that cart #2 completes the loop without leaving the track. Assume an elastic collision. (b) Find the height needed if instead the more massive...

Consider a solid sphere of mass m and radius r being released down a ramp from...

Consider a solid sphere of mass m and radius r being released down a ramp from a height h (i.e., its center of mass is initially a height h above the ground). It rolls without slipping and passes through a vertical loop of radius R. a. Determine the moment of inertia of the solid sphere. You must carry out the integration and it’s not sufficient just to write out 2/5mr^2 b. Use energy conservation to show that the tangential and...

A 2.2 kg cart slides eastward down a frictionless ramp from a height of 1.5 m...

A 2.2 kg cart slides eastward down a frictionless ramp from a height of 1.5 m and then onto a horizontal surface where it has a head-on elastic collision with a stationary 3.0 kg cart cushioned by an ideal Hooke’s Law spring. The maximum compression of the spring during the collision is 2.0 cm. [10 marks] a) Determine the velocity of the cart 1 just before the collision. [1 mark] b) At the point of maximum compression determine the velocity...

A block of mass m = 2.1 kg slides down a 36 ° inclined ramp that...

A block of mass m = 2.1 kg slides down a 36 ° inclined ramp that has a height h = 3.1 m. At the bottom, it hits a block of mass M = 7.1 kg that is at rest on a horizontal surface. Assume a smooth transition at the bottom of the ramp. If the collision is elastic and friction can be ignored, determine the distance the mass m will travel up the ramp after the collision.

an owl m=4.72kg slides down a semi-circular ramp r=7.5m. the owl starts at the top ramp...

an owl m=4.72kg slides down a semi-circular ramp r=7.5m. the owl starts at the top ramp at rest. when the owl is at an angle 31.9. what is the normal force exerted by the owl.

In the figure, a small block of mass m = 0.121 kg slides down a frictionless...

In the figure, a small block of mass m = 0.121 kg slides down a frictionless surface from an initial height of h = 0.850 m and then sticks to a uniform vertical rod of mass M = 0.879 kg and length L = 1.83 m. The rod pivots about point O through an angle θ before momentarily stopping. Find θ (in degrees).

Beginning from rest, an object of mass 200 kg slides down a 9-m-long ramp. The ramp...

Beginning from rest, an object of mass 200 kg slides down a 9-m-long ramp. The ramp is inclined at an angle of 20o from the horizontal. Air resistance and friction between the object and the ramp are negligible. Let g = 9.81 m/s2. Determine the kinetic energy of the object, in kJ, and the velocity of the object, in m/s, at the bottom of the ramp.

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The...

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The ball starts from rest. The ball descends a vertical height of 6.0 m to reach the bottom of the ramp. What is its speed at the bottom?

A solid, uniform disk of radius 0.250 m and mass 53.2 kg rolls down a ramp...

A solid, uniform disk of radius 0.250 m and mass 53.2 kg rolls down a ramp of length 4.70 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s

Subjects