The initial kinetic energy of a bike with mass m = 10 kg is 2000 J as it travels

Question

The initial kinetic energy of a bike with mass m = 10 kg is 2000 J as it travels in a horizontal road. the initial speed of the bike is If the bike stops in a time 0.5 s displacement of the bike is 7. A skier of mass. m=200 kg leaves the lop of a slope speed at the bottom of the slope is 13 m/s. (a) the height (b) the initial gravitational potential energy of the skier is ¦ A horizontal force of 100 N is applied to a 45-kg cart across a 10-m horizontal surface. (a) If the cart accelerates al 2 m/s^2, the work done by the 100 N force is ___ (b) the work done by the force of friction as it acts to retard the motion of the cart is A rock is thrown straight vertically upward with an initial velocity of 20 m/s. Ignore energy lost to air friction, (a) the rock will rise to a maximum height of (b) the velocity of the rock at half that maximum height is 10. A Hooke's law spring is compressed 24 cm from equilibrium and the potential energy stored is 72 J. (a) the spring constant in this case is (b) the spring is then used to launch a mass of 250 grams along a frictionless surface. the "launch speed" of the mass is

Explanation / Answer

6)a) K.E.= 0.5*m*v^2

2000= 0.5*10*v^2

v^2= 2000/5 = 400

v=20 m/s

b)Displacement= (u+v/2)*t = (0+20/2)*0.5 = 5 m

7) a) Change in Kinetic energy= Gravitational potential energy

0.5*m(13^2-5^2)= m*g*h

h= 7.34 m

b) Intial GPE= m*g*h= 200*9.8*7.34 = 14400 J

8) a) Work= force*displacement = 100*10= 1000 J

b) 100-f = 45*2

f= 10 N So work by friction= 10*10 = 100 J

9) a) Kinetic energy= gpe

0.5*m*20^2= m*9.8*h

h = 20.4 m

b) 0.5*m*20^2= m*9.8*10.2+ 0.5*m*v^2

v= 14.36 m/s

10) a)Electic Potential energy= 0.5 *k *x^2

72=0.5*k*0.24^2

k=2500 N/m

b) energy conservation

72= 0.5*0.25*v^2

v=24 m/s

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