The picture below shows a block of mass 5.22 kg held against a spring of spring constant k compressed by a distance d = 28.3 cm on a frictionless ramp of length L. The ramp has an angle of 20∘. A distance x = 1.16 m separates the ramp from a landing area that is at the same height as the top of the ramp. A) If the mass leaves the end of the spring at a speed of 4.43 m/s , what is the spring constant of the spring? k = N/m

B) If the mass reaches the top of the ramp moving at speed 2.81 m/s , what is the length of the ramp?

Measure the length of the ramp from the starting point (compressed spring) as shown in the picture. L = m

C) Does the mass successfully jump the gap and land on the other side?

D) At what height h below the top of the ramp must the landing area be placed for the block to successfully clear the 1.16 m wide gap? h= ___ m

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.

Brutus, the dog, is pulling a bone to the left with a force of 20 n. lassie, another dog, is pulling a bone to the right with a force of 18n. what is the net force? a. b. c.