An object of mass M= 6.0 kg, initially at rest, is pressed against a spring with spring constant k =12,000 N/m, compressed a distance d = 0.12m from equilibrium. The mass and the spring are located at the top of a hill of height, h = 2.0 m. The mass is released and as the spring decompresses the mass slides down the frictionless hill and then encounters a horizontal patch of ground with unknown coefficient of kinetic friction μk. a. What is the speed of the mass just before it encounters the rough patch of ground? b. The mass comes to rest a distance L = 8 m after encountering the patch of ground. What is the coefficient of frictio

A block of mass m = 3.5 kg is attached to a spring with spring constant k = 580 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 26° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.13. In the initial position, where the spring is compressed by a distance of d = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero.a. If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion. L=

A 0.20-kg mass is attached to a string and then released from rest, swinging in an arc as a pendulum. At the bottom of it swing, where it is 0.80 m above the floor, the string is cut and the mass becomes a projectile. It stricks the floor 0.56 meters (horizontally) from the point it was cut. From what height was the mass originally released?

A 0.28 kg mass is held against a compressed spring with a spring constant of 2,446 N/m. The mass is initially at rest upon a horizontal surface and the spring force is directed parallel to the plane of the surface. If the coefficient of kinetic friction is 0.716, with what speed does the mass leave contact with the spring if the spring is initially compressed by 0.068 m?

A block of mass m = 2.00 kg situated on a rough incline at an angle of 8 = 37.0° is connected to a spring of negligible mass having a spring constant of 100 N/m (see the figure below). The pulley is frictionelss. The block is released from rest when the spring is unstretched. The block moves 10.0 cm down the incline before coming to rest. Find the coefficient of kinetic friction between block and incline. k = 100 N/m www 8 m

A bowling ball of mass m = 1.6 kg is resting on a spring compressed by a distance d = 0.36 m when the spring is released. At the moment the spring reaches its equilibrium point, the ball is launched from the spring into the air in projectile motion at an angle of θ = 38° measured from the horizontal. It is observed that the ball reaches a maximum height of h = 3.5 m, measured from the initial position of the ball. Let the gravitational potential energy be zero at the initial height of the bowling ball.   a. What is the spring constant k, in newtons per meter?  b. Calculate the speed of the ball, vo in m/s, just after the launch.

Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. True False

Let's say we have a spring with a constant of K= 300 N/m and this spring is attached to the incline at the top making an angle of θ=44.0° with the horizontal. Now, after we have this problem, there is a projectile that has a mass of 1 kg that is pointing up the plane. The initial position of this projectile is d = 1.3 m and it is from the end 0f a uncompressed spring. Answer the following questions: Let’s say the incline has no friction at all and given the kinetic energy for the projectile is 15 J. How much c0mpression will the spring receive? Let's say we have a coefficient of friction = 0.300 and the spring will have to c0mpress 1.10 the instant the projectile stops..in order for this to happen, what should be the initial speed of the projectile?

A mass of m = 0.500 kg slides across a horizontal frictionless counter with a speed vo= 0.300 m/s. It then runs into and compresses a spring of spring constant k-750 N/m. ୪୪୪୩ d O Weight, Normal, Spring Force, Friction O Weight, Spring Force, Friction O Weight, Normal, Spring Force O Weight, Normal, Friction Physics Principles (a) Pick all forces act on the spring-mass system as the mass compresses the spring. (b) Which of these forces do not do any work? C C -VO Weight, Normal Force, Spring Force Weight, Normal Force Normal, Spring Force Weight, Friction m

A block of mass M = 8 kg rests on a horizontal frictionless floor, and is connected to a vertical wall by a spring of force constant k = 200 N/m. When the spring is in its equilibrium position (neither stretched nor compressed), the block just touches a second lighter block of mass m = 4 kg at rest on the frictionless floor. The spring with mass M attached is now compressed by 0.1 m and released. The two blocks undergo a completely inelastic collision, i.e., they stick together after collision. Draw a diagram and define all relevant variables. Just before the collision, what is the velocity of mass MT Just after the collision, what is the common velocity of the two blocks? (What is the maximum stretching of the spring after the collision?: How long after the collision do the masses reach their first maximum stretch?