Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Relativistic mechanics wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Center of mass wikipedia , lookup
Specific impulse wikipedia , lookup
Classical central-force problem wikipedia , lookup
Hunting oscillation wikipedia , lookup
Work (physics) wikipedia , lookup
Mass versus weight wikipedia , lookup
PHY 131 Ch 1 – 6 Exam A Name A ball is shot from the ground into the air. At a height of 10 m, its velocity is v = 8.0 i + 6.0 j. (a) To what maximum height does the ball rise? What are the (b) magnitude and angle of the ball's velocity just before it hits the ground? ay = Δvy / Δt so it will drop 11.8 m |v| = (82 + 15.42)½ -10 = vf – v10m / Δt y = ½ g t2 |v| = 17.4 m/s 2 -10 = 0 – 6 / Δt 11.8 = 5 tbottom 2/2 t10m to top = 0.6 sec 8/8 tbottom = 1.54 sec 8/8 vave = Δy / Δt ½(6+0) = (ytop – 10m) / .6 ytop = 11.8 m 8/8 Or y = ½gt2 + voy t 10 = -5t2 + [20/t – 6] t t2 + 1.2 t = 2 t = 0.6 ± √2.36 t = 0.6 ± 1.54 sec vave = Δy / Δt ½( v0+6) = 10/t v0 = 20/t - 6 tan θ = -15.4 / 8 θ = 63 degrees below horizontal ay = Δvy / Δt 10 = vbottom – vtop / Δt 10 = vbottom – 0 / 1.54 vbottom = 15.4 m/s 8/8 vx is constant = 8 m/s Block B in the figure weighs 600 N. The coefficient of static friction between block and table is 0.20; angle θ is 30°; assume that the cord between B and the knot is horizontal. Find the maximum weight of block A for which the system will be stationary. Ff – FTx = 0 FTx = Ff 12/12 FTx = μ FN FTx = 0.2 (600) FTx =120 N FTy – FWA = 0 FTy = FWA 12/12 tan θ = Fy / Fx 9/9 FTy = FTx tan θ FTy = 69.3 N 69.3 N = FWA We see that And Ff – FTx = 0 FTy – FWA = 0 Why? ΣF = m a, if a = 0 then forces to the left = right and forces up = down. A roller-coaster car has a mass of 500 kg when fully loaded with passengers. (a) if the car has a speed of 20 m/s at bottom of the 10 m radius drop, what is the force exerted by the track on the car at this point? (a) 13/13 10/10 (b) What is the maximum F – mg = m v2 / r N speed the car can have at the FN – 5000 = 500 202/10 top of the 15 m peak and still FN = 25000 N remain on the track? (b ) 10/10 FN + mg = mv2/r Where FN goes to zero mg = mv2/r v = 12.2 m/s PHY 131 Ch 1 – 6 Exam B Name At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displaced d = 50 m horizontally and h = 70 m vertically above the launch point. At the instant it reaches its maximum height above ground level, what is its horizontal displacement D from the launch point? y = ½ a t2 +vyt +0 70 = -5*22 +vy2 +0 vy = 45 m/s 10/10 x = ½ at2 +vxt +0 50 = 0 +vx2 +0 vx = 25 m/s a = Δv / Δt -10 = (vf – 45) / ttop ttop = 4.5sec 8/8 8/8 vave = Δx / Δt 25 = Δx / 4.5 Δx = 112.5 meters 7/7 A student of weight 800 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force on the student from the seat is 700 N. (a) What is the magnitude of the normal force at the lowest point? (b) If the wheel's speed is doubled, what is the magnitude FN at the highest point? Top (b) 13/13 2 FC = m(2v) /r = 400 N mg – FN = 400 N 800 – FN = 400 N FN = 400 N Bottom mg – FN = mv2/r 800 - 700 = mv2/r FC = mv2/r = 100 N 10/10 FN – mg = mv2/r FN – 800 = 100 FN = 900 N 10/10 A rocket of negligible mass moving in the horizontal direction becomes attached a block pulley system. Block A has mass of 3 kg, and Block B has a mass of 2 kg. The ramp is 30 degrees above the horizontal. What thrust must the rocket exert to cause the block system to accelerate up the ramp at a rate of 3 m/s2 if the frictional coefficient between block A and the ramp is 0.2? cos30 FThrust 5/5 FNet = mT a – sin30mAg – mB g – Ff = (mA + mB ) a 5/5 5/5 14/14 5/5 cos30 FThrust – 15 – 20 – Ff = (3 + 2) 3 cos30 FThrust – μ FN = 15 +20 +15 cos30 FThrust – .2 (sin30 FThrust + cos30mAg) = 50 N cos30 FThrust – .2 ( ½ FThrust + 26 ) = 50 N FThrust = 72 N