4.1
A 1,800 kg rescue truck travels east at 16 m/s while a 900 kg SUV travels west at 12 m/s on the same road. Treat east as positive. Calculate the momentum of EACH vehicle, then determine the combined momentum of the two-vehicle system and its direction.
Truck: +28,800 kg·m/s;
SUV: −10,800 kg·m/s.
Combined: +18,000 kg·m/s (east).
A 0.25 kg tennis ball approaches a racket moving left at 14 m/s and leaves moving right at 22 m/s. Contact lasts 0.030 s. Take right as positive. Find initial momentum, final momentum, impulse, and average net force.
pi = −3.5;
pf = +5.5 kg·m/s;
J = +9.0 N·s;
Favg = +300 N.
A 5.0 kg cart moving right at 6.0 m/s collides with a stationary 3.0 kg cart. The carts stick together on a nearly frictionless track. Find the total initial momentum, their shared final velocity, and the final momentum of the system.
pi = +30 kg·m/s;
vf = 30/8 = +3.75 m/s;
pf = +30 kg·m/s.
A 2.0 kg cart moves right at 4.0 m/s toward a stationary 3.0 kg cart. After the collision, the first cart moves right at 1.0 m/s and the second moves right at 2.0 m/s. Calculate total kinetic energy before and after, and classify the collision.
KEi = ½(2)(4²) = 16 J;
KEf = ½(2)(1²)+½(3)(2²) = 7 J.
Inelastic; 9 J transformed.
A 3.5 kg laboratory cart moves left with momentum −42 kg·m/s. A student loads another 1.5 kg onto the cart without changing its velocity. Determine the cart’s original velocity, its new total mass, and its new momentum. Take right as positive.
v = −42/3.5 = −12 m/s;
new mass = 5.0 kg;
new p = (5.0)(−12) = −60 kg·m/s.
A 1,600 kg car moving east at 20 m/s slows to 8.0 m/s east in 4.0 s. Find its initial and final momentum, the impulse from braking, and the average net force. Explain whether the force points east or west.
pi = +32,000;
pf = +12,800 kg·m/s;
J = −19,200 N·s;
Favg = −4,800 N (west).
A 6.0 kg cart travels right at 8.0 m/s toward a 4.0 kg cart moving left at 3.0 m/s. After they collide, the 6.0 kg cart moves right at 2.0 m/s. Determine the other cart’s final velocity and verify conservation of momentum.
pi and pf = 36 kg m/s
v2f = +6.0 m/s
Two 2.0 kg carts move right at 5.0 m/s and 1.0 m/s. After colliding, they move right at 1.0 m/s and 5.0 m/s, respectively. Calculate the total kinetic energy before and after. Is this collision elastic or inelastic?
KEi = ½(2)(25)+½(2)(1) = 26 J;
KEf = ½(2)(1)+½(2)(25) = 26 J.
Elastic.
Two delivery robots move along a hallway. Robot A has a mass of 24 kg and travels right at 3.5 m/s. Robot B has a mass of 18 kg and travels left at 5.0 m/s. Find each momentum and the total momentum. Explain why the system’s total is not the sum of the two magnitudes.
pA = +84 kg·m/s;
pB = −90 kg·m/s;
ptotal = −6 kg·m/s (left). Momentum is a vector.
A 0.18 kg hockey puck moves right at 9.0 m/s. A stick delivers an average 45 N force left for 0.060 s. Find the impulse, final momentum, and final velocity. Does the puck reverse direction?
J = −2.7 N·s;
pi = +1.62;
pf = −1.08 kg·m/s;
vf = −6.0 m/s. Yes, left.
Two students on rolling platforms approach each other. Student A (60 kg) moves right at 4.0 m/s, and student B (40 kg) moves left at 3.0 m/s. They hold on after colliding. Find their shared velocity and the velocity of the center of mass before and after.
pi = 240 − 120 = +120 kg·m/s;
vf = 120/100 = +1.2 m/s;
vcm before = after = +1.2 m/s.
A 4.0 kg cart moving right at 6.0 m/s sticks to a stationary 2.0 kg cart. Use conservation of momentum to find their shared final velocity. Then calculate total kinetic energy before and after and classify the collision.
vf = 24/6 = +4.0 m/s;
KEi = 72 J;
KEf = ½(6)(16) = 48 J.
Perfectly inelastic;
24 J transformed.
An asteroid fragment of mass 2.5 kg travels right at 18 m/s. Another fragment moves left at 6.0 m/s, and the total momentum of both fragments is +9.0 kg·m/s. Find the mass of the second fragment and show how the signs determine your answer.
m2 = 6.0 kg
A 3.0 kg cart moves right at 5.0 m/s. A net force of 24 N acts left for 0.75 s. Find the impulse, final momentum, and final velocity. Use your answer to determine whether the cart stops or reverses.
J = −18 N·s;
pi = +15;
pf = −3.0 kg·m/s;
vf = −1.0 m/s. Reverses left.
A 12 kg cart travels right at 7.0 m/s and an 8.0 kg cart travels left at 4.0 m/s. Find the velocity of their center of mass. Then predict whether the center-of-mass velocity changes when they collide if the net external impulse is negligible.
vcm = [12(7) + 8(−4)]/20 = +2.6 m/s;
it stays +2.6 m/s.
A 3.0 kg cart moving right at 4.0 m/s collides with a 1.0 kg cart moving left at 2.0 m/s. Afterward the 3.0 kg cart moves right at 1.0 m/s and the 1.0 kg cart moves right at 7.0 m/s. Compare total momentum AND total kinetic energy before and after. Classify the collision.
pi = 12 − 2 = +10;
pf = 3 + 7 = +10 kg·m/s.
KEi = 24 + 2 = 26 J;
KEf = 1.5 + 24.5 = 26 J.
Elastic.
A 12 kg test sled travels right at 7.0 m/s. It is then loaded to a total mass of 20 kg and moves left at 3.0 m/s. Calculate the initial and final momentum and the change in momentum of the sled system. Explain the meaning of the sign of Δp.
pi = +84 kg·m/s;
pf = −60 kg·m/s;
Δp = −144 kg·m/s. Change points left.
A 0.15 kg baseball travels left at 40 m/s and rebounds right at 50 m/s in 0.0050 s. Calculate the change in momentum and average net force. If the SAME change in momentum occurs over 0.015 s instead, find the new average force and compare the magnitudes.
J = +13.5 N·s;
F1 = +2,700 N;
F2 = +900 N. Tripling time reduces average force to one-third.
A 75 kg hockey player skates east at 9.0 m/s while a 60 kg player skates west at 5.0 m/s. After colliding, the first player moves west at 2.0 m/s. Find the second player’s final velocity, then calculate the momentum change of EACH player and explain the relationship.
pi = 675 − 300 = +375;
v2f = +8.75 m/s.
Δp1 = −825 kg·m/s;
Δp2 = +825 kg·m/s.
A 2.0 kg cart moving right at 8.0 m/s strikes a stationary 6.0 kg cart and the two stick. Calculate their shared final velocity, initial and final kinetic energies.
vf = 16/8 = +2.0 m/s;
KEi = 64 J;
KEf = 16 J;