A 3.62 kg ball is pushed against a horizontal spring whose force constant is 1126 N/m, compressing the spring to x=0.277 m. When the system is released, the ball traveled along the horizontal surface whose coefficient of kinetic friction is 0.203 and then up a frictionless plane inclined at 0=29.3° above the horizontal. If the ball has reached a distance of d=0.9 m along the plane before sliding back downwards, how far did the ball travel the moment it leaves the spring until it reached the bottom of the inclined? -x- d O 3.55 m O 1.29 m 3.83 m O 5.72 m x = 0

As shown below, a box with a mass of 1.00 kg is released from rest at point A. It travels down a frictionless quarter-circle arc to point B. It slides on a horizontal track from B to C where it compresses a spring a distance of 85.2 cm before stopping. The horizontal track from B to C is 1.63 m long and has a constant 2.8 N frictional force acting on the box as it slides from B to when it stops. Find the spring constant of the spring in N/m. m = 1.0 kg A| r= 2.0 m B C

A 5.40-kg block is set into motion up an inclined plane with an initial speed of v; = 8.20 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of 0 = 30.0° to the horizontal. (a) For this motion, determine the change in the block's kinetic energy. J (b) For this motion, determine the change in potential energy of the block-Earth system. J (c) Determine the friction force exerted on the block (assumed to be constant). N (d) What is the coefficient of kinetic friction?

A bowling ball of mass m = 1.2 kg is launched from a spring compressed by a distance d = 0.31 m at an angle of θ = 36° measured from the horizontal. It is observed that the ball reaches a maximum height of h = 4.6 m, measured from the initial position of the ball. Let the gravitational potential energy be zero at the initial height of the bowling ball. what is the spring constant k, in newtons per meters? k = ?

A single conservative force F(x) acts on a 3.2 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is given by U(x) = - 3xex/ 4 where U is in Joules and x is in meters. At x = 4 m the particle has a kinetic energy of 7.7 J. (a) What is the mechanical energy of the system? (b) What is the maximum kinetic energy of the particle and (c) the value of x at which it occurs? (a) Number i Units (b) Number Units (c) Number i Units

A box is pressed against a horizontal spring, compressing the spring from its relaxed length. The box is then released and the spring launches the box horizontally along a track that ends in a ramp, as shown above. The box has enough speed to leave the ramp, and the box reaches a maximum vertical height above the floor. Assume there is negligible friction between the box and the track and air resistance is negligible.   K = spring constant of spring X = distance the spring is compressed M = mass box Theta = angle of ramp from horizontal H = maximum height reached by box   The scenario is repeated using a different box with a greater mass. The spring is compressed the same distance x.   Indicate how h in this second scenario compares to h in the original scenario, and explain why without mathematically deriving a relation for h. Students derive an equation for h in the original scenario, h= (sin2theta)kx2/2Mg, which may or may not be correct. Is this equation consistent with your claim…

A 1400 kg car begins sliding down a 15.0 ° inclined road with a speed of 33.0 km/h.The engine is turned off, and the only forces acting on the car are a net frictional force from the road and the gravitational force. After the car has traveled 53.0 m along the road, its speed is 44.0 km/h. (a) How much is the mechanical energy of the car reduced because of the net frictional force? (b) What is the magnitude of that net frictional force?

You throw a tennis ball (mass 0.0570 kg) vertically upward. It leaves your hand moving at 15.0 m/s. Air resistance cannot be neglected, and the ball reaches a maximum height of 8.00 m. (a) By how much does the total mechanical energy decrease from when the ball leaves your hand to when it reaches its maximum height? (b) What is the magnitude of the average force of air resistance?

A certain spring is found not to obey Hooke's law; it exerts a restoring force F(x) = -ax² - 6x³ if it is stretched or compressed, where: a = 10.0N/m², B = 300.0N/m³ The mass of the spring is negligible. Calculate the potential energy function U(x) for this spring, if U(x=0) = 0. Find the spring potential energy at x = 0.500 m

A box with 14 kg of mass slides down an inclined plane that is 1.8 m high and 3.9 m along the inclined plane. Due to friction the box reaches 4.6 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with 750 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction When the box is temporarily stopped by the spring, how much is the spring compressed in m? Hint: start from the bottom of the inclined plane since you know the speed of the box there. Not all values must be used.