A car of mass 1000 kg is at the top of a 10 Degree hill as shown. a. What is its

Question

A car of mass 1000 kg is at the top of a 10 Degree hill as shown. a. What is its gravitational potential energy relative to the bottom of the hill? b. If the car rolls down the hill (with the engine off) with negligible friction and air resistance, what will its kinetic energy be when it reaches the bottom? c. Suppose instead that the amount of work done on the car by the frictional and air resistance forces as the car rolls down the hill is 50,000 J. What then is the kinetic energy of the car when it reaches the bottom of the hill? The graph on the right is of the force exerted by a spring as a function of the distance it is stretched from its unstretched length. Show calculations for each part below. a. What is the spring constant of this spring? b. What is the elastic potential energy if the spring is stretched 1.5 m from its equilibrium length? c. A low-friction cart of mass 5.0 kg is attached to the spring, the spring is stretched 1.5 m from its equilibrium length, and then the cart is released. What is the kinetic energy of the cart just as the spring passes through its equilibrium length? What is the velocity of the cart at this position?

Explanation / Answer

Q.5 a) PE = mgh

h= 50 m tan 10= 8.816 m

pE = 1000 (9.8) ( 8.816) =86400.2205 J

b ) KE = 86400.2205 J

c)KE = 86400.2205 J- 50,000J= 36400.2205J

Q.6 )

F = Kx ( hooke's law)

K = slope of f-x curve=(12-0)/ (4.5-0)=2.67 N/m

b) E = 1/2 kx^2= 0.5 ( 2.67) (1.5^2)=3 J

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