Units and quantities
What is the unit of mechanical work?
Joule (J).
Write the equation for calculating the work done by an object.
W = F*s
Calculate the work done by picking up a bucket of water of mass 10 kg to the height 65 cm from the ground.
W = Fs = mgh = 10*9,81*0,65 = 63,765 J
What is the unit of efficiency?
No unit is used.
Write the equation for calculating the potential energy of an object.
E = mgh
Ek = 1/2 mv2 = 1/2*1000*(25)2 = 312 500 J
What is the difference between average power and instantaneous power?
Average power - work done W in some time t. Instantaneous power - force F needed to move object with speed v.
Write the equation for calculating efficiency using different quantities.
efficiency = P/P0 = W/W0 = E/E0
A bullet of mass 40 g hit a tree and penetrated to a depth of 15 cm. How fast was it moving before the impact, if the resistance force of the wood of the tree is 5 kN?
Ek = 1/2 mv2 and W = F*s
v = odmocnina (2Fs/m) = odmocnina (2*5000*0,15/0,04) = 193,65 m/s
Prove that unit of mechanical work in SI units is kg*m2*s-2.
W = Fs = mgs => [W] = kg*m*s-2*m = kg*m2*s-2.
Prove that potential energy and work done can be calculated by the same equation.
W = Fs = FGh = mgh = Ep
A train is moving with a constant speed developing a tractive force of 70 kN at a power 2000 kW. How long does it take to cover 60 km track?
t = Fs/P = (70 000*60 000)/2000000 = 2100
Prove that the unit of kinetic energy and the unit of potential energy is the same.
Ep = mgh => [Ep] = kg*m*s-2*m = kg*m2*s-2
Ek = 1/2 mv2 => [Ek] = kg*(m*s-1)2 = kg*m2*s-2
Derive an equation for kinetic energy from the equation used for calculating the work done.
W = Fs = F*1/2*a*t2 = m*a*1/2*a*t2 = 1/2*m*a2*t2 = 1/2*m*(at)2 = 1/2*m*v2
A ball of mass 40 g was falling down from the height 70 cm with initial speed 1,5 m/s. To what height did the ball jump after hitting the table?
Ek0 + Ep0 = Ep1
1/2mv2 + mgh0 = mgh1
h1 = (1/2mv2 + mgh0) / mg = (1/2*0,04*1,52 + 0,04*9,81*0,7) / 0,04*9,81 = 0,815 m