A block of mass m=1.9kg is released from rest at an unknown height h. The coefficient of friction between the block and the incline oriented at an angle of 0 =530 is Hk=0.16. Assume the circular part of the track is frictionless and the radius of the track is R=0.52m. Find the minimum height h, for the block to remain in contact with the track at all times, even at the top of the circular loop. Take g =9.81m/s² and express your final result using two decimal places. m R. h

A 7.80 g bullet is initially moving at 650 m/s just before it penetrates a tree trunk to a depth of 4.70 cm. (a) What is the magnitude of the average frictional force (in N) that is exerted on the bullet while it is moving through the tree trunk? Use work and energy considerations to obtain your answer.   b)  Assuming the frictional force is constant, how much time (in s) elapses between the moment the bullet enters the tree trunk and the moment it stops moving?

A brick of mass m is initially at rest at the peak of an inclined plane which has a height of 5.52m and has an angle of θ=20.3∘ with respect to the horizontal. After it has been released, it is found to be traveling at v=0.84m/s a distance d after the end of the inclined plane, as shown. The coefficient of kinetic friction between the brick and the plane is μp=0.1, and the coefficient of friction on the horizontal surface is μr=0.2. What is the speed of the brick, in meters per second, just after it leaves the inclined plane? Find the distance, d, in meters.

A block weighing 2.50 kg begins its motion from a stationary position at point A, located at the highest point of a frictionless ramp. The ramp is inclined at an angle of 40° relative to the horizontal and has a length of 1.50 m. As the block slides down the ramp, it reaches a region between point B and point C, which is a rough horizontal surface with a kinetic friction coefficient of 0.30. After covering a distance of 1.00 m on the horizontal surface, the block encounters a lightweight spring with a spring constant of 900 N/m. By employing the work-energy theorem, determine the velocity of the block at point C just before it collides with the spring?

A 1.5-kg box is released from rest on a frictionless surface that is sloped at θ = 35◦ above the horizontal.After sliding 1.0 m down the slope, the box transitions smoothly to a rough, horizontal surface, slides forsome distance, and then comes to a stop. If the coefficient of kinetic friction between the box and thehorizontal surface is 0.12, how far along the horizontal surface does the box travel?

A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.79 m. With the string hanging vertically, the object is given an initial velocity of 2.8 m/s parallel to the ground and swings upward in a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle with its initial vertical orientation and then swings back downward. Find the angle 0. Number i Units

A block slides along a track with an initial velocity vo = 7.0 m/s from one level to a higher level after passing through an intermediate valley. The difference h from the initial position to the elevated track is 0.89 m. The track is frictionless until reaches the top. There (at the top), a frictional force stops the block in a distance d. The coefficient of kinetic friction  between the block and the surface is 0.60. Find the distance d.

The Super Sled travels with an initial kinetic energy of 3369 J horizontally and to the right along a frictionless flat surface, initially at a height of zero (initial gravitational potential energy = 0). The driver briefly engages the rocket over a distance (Ax) of 2.000 m, pushing the sled with a force of 400.0 N over that distance. The rocket is then turned off. The sled then goes up an inclined surface with a rough surface. The coefficient of kinetic friction on the incline is uk. At the top of the incline, the sled reaches a height h = 1.500 m above the ground where the surface becomes flat and frictionless again. The sled (including the rocket and driver) has a total mass of 87.00 kg. (Notes: assume that g = 9.810 m/s² , and that the mass of fuel used by the rocket is negligible. Do not use scientific notation). After &, rocket rocket Before propulsion propulsion starts ends rough inclined surface rocket frictionless engaged coefficient of kinetic friction = H surface h = 1.500 m…

A block of mass, m = 0.5 kg is used to compress a spring with a spring con- 78.4 N/m a distance x from it's resting point. The block is then stant, k released and travels towards a circular loop of radius, R = 1.5 m. The loop and the surface as frictionless except for the region, of length 2.5 m, defined by AB which has a coefficient of friction, µk = 0.3. Determine the minimum compression of the spring that allows for the block to just make it through the loop-to-loop at point C (Hint: This problem is best done by starting at the end and working backwards). R k A В

A crate of mass m is initially at rest at the highest point of an inclined plane which has a height of 5.28 m and makes an angle of A = 17.2° with respect to the horizontal. After it has been released, it is found to be traveling at v = 0.29 m/s a distance dafter the end of the inclined plane, as shown. The coefficient of kinetic friction between the crate and the plane is tp = 0.1, and the coefficient of friction on the horizontal surface is f4r = 0.2.