Energy
A man returning from a successful ice fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the man exerts a force of magnitude 120 N on the sled by pulling on the rope.
How much work does he do on the sled if the rope is horizontal to the ground and he pulls the sled 5.00 m?
W= f*d = 120*5 = 600 J
An airboat with mass 350 kg has an engine that produces a net horizontal force of 770 N, after accounting for forces of resistance.
Find the acceleration of the airboat.
770 = 350 * a
A = 2.2 m/s^2
The rotor on a helicopter turns at an angular velocity of 320 revolutions per minute. Express this angular velocity in radians per second.
320 rev/min * 1min/60s * 2πrad/1rev = 33.5103 rad/s
A block on the end of a horizontal spring is pulled from equilibrium at x 5 0 to x 5 A and released. Through what total distance does it travel in one full cycle of its motion? (a) A/2 (b) A (c) 2A (d) 4A
(D)
Two masses m 1and m2, with m 1, m2, have equal kinetic energy. How do the magnitudes of their momenta compare? (a) Not enough information is given. (b) p 1 < p 2 (c) p 1 = p 2 (d) p 1 > p 2
(B)
KE = 1/2mv^2 = p^2/(2m)
P = mv
A man returning from a successful ice fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the man exerts a force of magnitude 120 N on the sled by pulling on the rope.
How much work does he do on the sled if θ = 60.0° and he pulls the sled 5.00 m? (Treat the sled as a point particle, so details such as the point of attachment of the rope make no difference.)
W = f * d*cosθ = 120 * 5 * cos(60) = 600*1/2 = 300 J
An airboat with mass 350 kg has an engine that produces a net horizontal force of 770 N, after accounting for forces of resistance.
Starting from rest, how long does it take the airboat to reach a speed of 12.0 m/s?
A = 2.2 m/s^2
12 = 0 + 2.2(t)T = 5.45454545 s
The rotor on a helicopter turns at an angular velocity of 320 revolutions per minute. If the rotor has a radius of 2.00 m, what arc length does the tip of the blade trace out in 300 s?
33.5103 rad/s * 300 s = 10053.09 rad
Arc length = θr = 10053.09*2 = 20106.19 m
For a simple harmonic oscillator, which of the following pairs of vector quantities can’t both point in the same direction? (The position vector is the displacement from equilibrium.) (a) position and velocity (b) velocity and acceleration (c) position and acceleration
(C)
A golf ball with mass 0.05 kg is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is maximally deformed) and then back to zero when the ball leaves the club. Assume that the ball leaves the club face with a velocity of 44 m/s. Find the magnitude of the impulse due to the collision.
I = ∆p = 0.05*44 - 0 = 2.2 kg * m/s
A man returning from a successful ice fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the man exerts a force of magnitude 120 N on the sled by pulling on the rope.
At a coordinate position of 12.4 m, the man lets up on the applied force. A friction force of 45.0 N between the ice and the sled brings the sled to rest at a coordinate position of 18.4 m. How much work does friction do on the sled?
Wfriction = -45 * (18.4-12.4) = -270 J
An airboat with mass 350 kg has an engine that produces a net horizontal force of 770 N, after accounting for forces of resistance.
After reaching 12 m/s, the pilot turns off the engine and drifts to a stop over a distance of 50.0 m. Find the resistance force, assuming it’s constant.
0 = 12^2 + 2(a)(50)
A = -1.44 m/s^2
Force of resistance = 350 * -1.44 = -504 N
The rotor on a helicopter turns at an angular velocity of 320 revolutions per minute. The pilot opens the throttle, and the angular velocity of the blade increases while rotating twenty-six times in 3.60 s. Calculate the average angular velocity during that time.
Avg angular velocity = ∆θ/∆t = 52π/3.6 = 45.37856 rad/s
∆θ = 26 rev * 2π = 52π
When an object moving in simple harmonic motion is at its maximum displacement from equilibrium, which of the following is at a maximum? (a) velocity, (b) acceleration, or (c) kinetic energy
(B)
A golf ball with mass 0.05 kg and radius of 0.02 m is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is maximally deformed) and then back to zero when the ball leaves the club. Assume that the ball leaves the club face with a velocity of 44 m/s. Estimate the duration of the collision and the average force acting on the ball.
Displacement = the radius of the golf ball
Velocity average = ∑v/2 = (44+0)/2 = 22 m/s
The driver of a 1000 kg car traveling on the interstate at 35.0 m/s (nearly 80.0 mph) slams on his brakes to avoid hitting a second vehicle in front of him, which had come to rest. After the brakes are applied, a constant kinetic friction force of magnitude 8000 N acts on the car. Ignore air resistance.
At what minimum distance should the brakes be applied to avoid a collision with the other vehicle?
∑w = 1/2 mvf^2 - 1/2 mvi^2
Friction force * displacement = -8000* displacement = 0 - 1/2(1000)(35)^2
Displacement = 76.5625 m
A block having a mass of 4.00 kg rests on a slope that makes an angle of 60.0° with the horizontal. If the coefficient of static friction between the block and the surface it rests upon is 0.650, calculate
(a) the normal force, (b) the maximum static friction force, and (c) the actual static friction force required to prevent the block from moving.
(a) force of normal equals mgcosθ = 4(9.81)cos(60) = 19.62 N
(b) static friction force = µ*normal force = 0.65 * 19.62 = 12.753 N
(c) actual static friction force = mgsinθ = 4(9.81)sin(60) = 33.9 N
A wheel rotates with a constant angular acceleration of 3.50 rad/s^2. If the angular velocity of the wheel is 2.00 rad/s at t = 0 through what angle does the wheel rotate between t = 0 and t = 2.00 s? Give your answer in radians and in revolutions.
Δθ = ωi(t)+1/2(α)(t)^2 = 2(2) + 1/2(3.5)(4) = 4 + 7 = 11 rad
An object of mass m is attached to a horizontal spring, stretched to a displacement A from equilibrium, and released, undergoing harmonic oscillations on a frictionless surface with period T0 . The experiment is then repeated with a mass of 4m. What’s the new period of oscillation? (a) 2T 0 (b) T 0 (c) T0 /2 (d) T0 /4
(A)
A golf ball with mass 0.05 kg and radius of 0.02 m is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is maximally deformed) and then back to zero when the ball leaves the club. Assume that the ball leaves the club face with a velocity of 44 m/s. Estimate the average force acting on the ball.
I = F*t = ∆p = 0.05*44 - 0 = 2.2 kg * m/s
T = displacement/velocity average = 0.02/22 = 0.000909 s
Displacement = the radius of the golf ball
Velocity average = ∑v/2 = (44+0)/2 = 22 m/s
F = I/t = 2.2/ 0.000909 = 2420.242 N
The driver of a 1000 kg car traveling on the interstate at 35.0 m/s (nearly 80.0 mph) slams on his brakes to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the brakes are applied, a constant kinetic friction force of magnitude 8000 N acts on the car. Ignore air resistance.
If the distance between the vehicles is initially only 30.0 m, at what speed would the collision occur?
-8000*30 = 1/2 (1000) (vf)^2 - 1/2 (1000) (35)^2
Vf = 27.2946 m/s
A block having a mass of 4.00 kg rests on a slope that makes an angle of 60.0° with the horizontal. If the coefficient of static friction between the block and the surface it rests upon is 0.650.
Will the block begin to move or remain at rest?
No because the static friction with µ = 0.65 only provide a static friction force of 19.62 N while the static friction needed for the block to remain at rest is 33.98 caused by gravity.
A wheel rotates with a constant angular acceleration of 3.50 rad/s^2. If the angular velocity of the wheel is 2.00 rad/s at t = 0
(a) What is the angular velocity of the wheel at t = 2.00 s? (b) What angular displacement results while the angular velocity found in part (a) doubles?
(a) Angle Acceleration =Δω/∆t = 3.5 = (ωf-2)/2
ωf = 9 rad/s
(b) ωf^2 = ωi^2 + 2α∆θ = 324 = 4 + 7∆θ
∆θ = 45.7142 rad
An object of mass m is attached to a horizontal spring, stretched to a displacement A from equilibrium, and released, undergoing harmonic oscillations on a frictionless surface with period T0 . The experiment is then repeated with a mass of 4m. What’s the new period of oscillation? Is the subsequent total mechanical energy of the object with mass 4m (a) greater than, (b) less than, or (c) equal to the original total mechanical energy?
(C)
In a crash test, a car of mass 1500 kg collides with a wall and doesn’t rebound off the wall. The initial velocity of the car are vi = -15.0 m/s. If the collision lasts for 0.150 s, find the average force exerted on the car.
Impulse = F*t = ∆p
I = 1500(0) + 15(1500) = 22500 N * s = F * 0.15
F = 150000 N