Problem 5: A block of mass 4.2 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 490 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 39⁰

A block of mass m is located on an inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is μ₁. The block presses against, but is not attached to, a spring with constant k₁. When the spring is at its equilibrium position, the block is at a height h above the ground, as shown. The initial position of the block, from which it is released, is a bit further up the inclined plane such that the spring is initially compressed by Ax. At the bottom of the inclined plane is a horizontal plane with a different coefficient of friction, μ2, for the first distance, d, after which the surface is frictionless, and the equilibrium position of a spring with constant k₂ is encountered. Part (a) Suppose that numeric values are such that block comes to rest before reaching the the ramp. Let x distance traveled from the equilibrium position of the block towards the bottom of the ramp. Enter an expression for x. Part (b) Suppose…

You have a light spring which obeys Hooke's law. This spring stretches 2.24 cm vertically when a 2.40 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) 1050 N/m (b) the distance (in cm) the spring stretches if you replace the 2.40 kg object with a 1.20 kg object 1.12 cm (c) the amount of work (in J) an external agent must do to stretch the spring 8.50 cm from its unstretched position 758.625 X J

A 1120-kg car is being driven up a 7.03 ° hill. The frictional force is directed opposite to the motion of the car and has a magnitude of 490 N. A force F is applied to the car by the road and propels the car forward. In addition to these two forces, two other forces act on the car: its weight W and the normal force FN directed perpendicular to the road surface. The length of the road up the hill is 281 m. What should be the magnitude of F, in Newtons, so that the net work done by all the forces acting on the car is 188 kJ?