A freight company uses a compressed spring to shoot 1.70 kg packages up a 1.00-m-high frictionless ramp into a truck, as (Figure 1) shows. The spring constant is 417 N/m and the spring is compressed 30.0 cm.

A 200-g steel ball is tied to a 2.00m “massless” string and hung from the ceiling to make a pendulum, and then, the ball is brought to a position making a 30 angle with the vertical direction and released from rest. Ignoring the effects of the air resistance, find the speed of the ball when the string (a) is vertically down, (b) makes an angle of 20 with the vertical and (c) makes an angle of 10 with the vertical.

“ E=K+Uconstant is a special case of the work energy theorem.” Discuss this statement.

An electric scooter has a battery capable of supplying 120 Wh of energy. If friction forces and other losses account for 60.0% of the energy usage, what altitude change can a rider achieve when driving in hilly ter-rain if the rider and scooter have a combined weight of 890 N?

Calculate the power output needed for a 950-kg car to climb a 2.00 slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N.

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150 N. If the mass of the arrow is 50 g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?

A 6.50 102-kg elevator starts from rest and moves upward for 3.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upward trip with constant speed?

A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people ‘would it take to nm a 4.O0-kW electric clothes dryer? (b) How many people would it take to replace a large electric power plant that generates 800 MW?

(a) What is the power output in watts and horsepower of a 70.0-kg sprinter who accelerates from rest to 10.0 m/s in 3.00 s? (b) Considering the amount of power generated, do you think a well-trained athlete could do this repetitively for long periods of time?

A freight company uses a compressed spring to shoot 1.60 kg packages up a 1.00-m -high frictionless ramp into a truck, as the figure(Figure 1) shows. The spring constant is 321 N/m and the spring is compressed 33.0 cm. What is the speed of the package when it reaches the truck?