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a freight company uses a compressed spring to shoot 1.80 kg packages up a 1.00-m -high frictionless ramp into a truck, as the figure(figure 1) shows. the spring constant is 343 n/m and the spring is compressed 34.0 cm .
a freight company uses a compressed spring to shoot 1.80 kg packages up a 1.00-m -high frictionless ramp into a truck, as the figure(figure 1) shows. the spring constant is 343 n/m and the spring is compressed 34.0 cm .
Using conservation of energy, the speed of the package when it reaches the truck is approximately 1.0 m/s.To determine the speed of the package as it reaches the truck, we'll need to use the conservation of mechanical energy principle. Since there's no friction on the ramp, the only forces doing work are the spring force and gravity. The initial potential energy stored in the compressed spring will be converted into gravitational potential energy as the package moves up the ramp, and the remainder will be kinetic energy when it reaches the truck.The spring potential energy (PE-spring) can be calculated using the formula PE-spring = 0.5 × k × x², where 'k' is the spring constant and 'x' is the compression distance. The gravitational potential energy (PE-gravity) at the height 'h' is given by PE-gravity = m × g × h, where 'm' is the mass of the package, and 'g' is the acceleration due to gravity. Conservation of energy states that PE-spring = PE-gravity + KE, where KE is the kinetic energy of the package.Substituting the known values, we have:0.5 × 343 N/m × (0.34 m)² = 1.80 kg × 9.81 m/s² × 1.00 m + 0.5 × 1.80 kg × v²After calculations:v = {2 × (PE-spring - PE-gravity)}/{m})1/2 = {2 × (19.6422 J - 17.658 J)}/ {1.80 kg})/1/2v ≈ 1.0 m/s...