Mechanical Energy Practice Test

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		Practice Test Mechanical Energy
		Assume magic land conditions on all problems unless stated otherwise. In other words there is no air resistance or friction.
		Indicate the best answer:
1	)	Bill throws a rock straight up at a velocity = 10 m/s. How high does it go? 1/2 mv_o² = mgh h = v_o² / (2g) = (10m/s)² / ( 2 ∙ 10 m/s²) = 5 m
2	)	A cannon ball is shot upward at a velocity of 220 m/s. When it eventually falls back to the same level it started from, it has a velocity of 200 m/s. What % of the energy was lost as heat? heat = 1/2 mv_o² - 1/2 mv_f² = 1/2 m (200² - 220²) % lost as heat = [1/2 m (200² - 220²)] / (1/2 m 220²) x 100% = (200² - 220²) / (220²) x 100% = 17 %
3	)	A 200 kg motorcycle traveling at 20 m/s and suddenly speeds up to 30 m/s. How much work was done? W = Δk = 1/2 m (30² - 20²) = 50,000 j
4	)	Find the minimum power required for a person to drive a car at a constant speed of 30.0 m/s up a 30 degree slope. Assume the mass of the person and car = 1000 kg power = Fv = (mg sin 30) v = (1000 kg ∙ 10 m/s/s ∙ 0.5) ∙ 30 m/s = 150,000 w
5	)	A box of mass m sits on top of a nonlinear spring which is compressed below its equilibrium point by a distance x. How high will the box go when it is released? The spring's equation is: F = -kx^3. Note: the box is not attached to the spring U = - ∫ F_(x) ∙ dx = - ∫ -kx^3 ∙ dx = 1/4 kx^4 define U_g= 0 at the lowest point ΔU_s - ΔU_g= 0 ΔU_s = ΔU_g 1/4 kx^4 = mgh h = (1/4 kx^4) / (mg)
6	)	How much work does the gravity of a planet do on a satellite as it orbits ? zero
7	)	Superman pushes on a box with force of 1000 Newtons. His force makes an angle of 60 degrees with the horizon. The box moves 5 meters at a constant velocity of 40 m/s. How much work is done by the friction force acting on the box. Assume no air resistance force. 2500 joules
8	)	For a non linear spring U_s= 7 x^3 +2x^2. Find an expression for the force as a function of x. F_(x)= - dU / dx F = -21 x^2 - 4x
9	)	A nonlinear spring has the following relationship between force and displacement of the spring from its equilibrium: F = - 3 x^3 - 2 x^2 - 3x. Find the amount of energy stored in the spring if it is compressed by 1/4 meter. U = - ∫ F_(x)∙ dx = 23 1/3
10	)	Jane attaches an unknown mass to a linear spring with a spring constant k. She measure the period of the spring and mass system at time = T. What is the mass of the meteor? T = 2p(m / k)^0.5 T² = 4p²(m / k) m = (kT²) / (4p²)
11	)	Two large wheels move down equal slopes. One has friction and the other doesn't. Which wheel has the highest linear velocity at the bottom? The wheel with no friction because it does not rotate and hence all the change in potential energy goes into linear kinetic energy.
12	)	A force 6i, 7j, -2k Newtons pushes on a mass and displaces it an amount 2i, -3j, 4k meters. What is the change in kinetic energy for the mass? - 17 Joules
13	)	A pendulum has a velocity of v at its lowest point. How high will it swing up in the vertical dimension? h = v² / (2g)
14	)	Bob throws a rock with a mass of m off a cliff of height = h. The rock's initial velocity = v_o. What is the velocity of the rock just before it hits the ground? v = ( v_o² + 2gh)^0.5
15	)	Robin Hood fires his bow straight up to a height = h_o. He then fires it at a 30 degree angle with respect to the horizontal. How high does it go? 1/4 h_o
16	)	A box starts from rest and slides a vertical distance = h down a 29 degree slope. At the bottom velocity = (0.64gh )^0.5. How much energy was dissipated as heat? 0.68mgh
17	)	Bob is driving his scooter at 20 m/s and slows down to 10 m/s over a 5 second period. How much mechanical energy was converted to heat? 150m, (note: m = the mass of the scooter)

		Online Quiz - Mechanical Energy